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You could as well say

"Ich konnte das nicht tun."

instead of

"Das konnte ich nicht tun."

which counts against your argument (emphasis mine)

As a native English speaker myself, in comparison with German, English appears to be much more "Speaker centric" ... .

I have noticed this pattern for a long time, but as of now, I still have failed to come up with a pattern I could remember that would guide me as to when and where I should put certain sentence elements on the two sides of the primary verb.

Können is an auxiliary verb in that sentence. The primary verb is tun.

The verb always appears at the second position as @CarstenS mentioned in their comment.

You can check this at the link https://en.wikipedia.org/wiki/V2_word_order .

Can someone explain how German speakers think about sentence elements in a way that tells me where I should put the main sentence elements? Most notably, the two primary actors that reside on the left and right side of a sentence's primary verb?

It may be a concern of emphasis that Das is placed before the ich in your example.

Also your doubts of Yoda Speech don't really apply, in German translations it would be rather

"Nicht tun konnte ich das."

You could as well say

"Ich konnte das nicht tun."

instead of

"Das konnte ich nicht tun."

which counts against your argument (emphasis mine)

As a native English speaker myself, in comparison with German, English appears to be much more "Speaker centric" ... .

I have noticed this pattern for a long time, but as of now, I still have failed to come up with a pattern I could remember that would guide me as to when and where I should put certain sentence elements on the two sides of the primary verb.

Können is an auxiliary verb in that sentence. The primary verb is tun.

The verb always appears at the second position as @CarstenS mentioned in their comment.

You can check this at the link https://en.wikipedia.org/wiki/V2_word_order .

Can someone explain how German speakers think about sentence elements in a way that tells me where I should put the main sentence elements? Most notably, the two primary actors that reside on the left and right side of a sentence's primary verb?

It may be a concern of emphasis that Das is placed before the ich in your example.

Also your doubts of Yoda Speech don't really apply, in German translations it would be rather

"Nicht tun konnte ich das."

You could as well say

"Ich konnte das nicht tun."

instead of

"Das konnte ich nicht tun."

which counts against your argument (emphasis mine)

As a native English speaker myself, in comparison with German, English appears to be much more "Speaker centric" ... .

I have noticed this pattern for a long time, but as of now, I still have failed to come up with a pattern I could remember that would guide me as to when and where I should put certain sentence elements on the two sides of the primary verb.

Können is an auxiliary verb in that sentence. The primary verb is tun.

The verb always appears at the second position as @CarstenS mentioned in their comment.

You can check this at the link https://en.wikipedia.org/wiki/V2_word_order .

Can someone explain how German speakers think about sentence elements in a way that tells me where I should put the main sentence elements? Most notably, the two primary actors that reside on the left and right side of a sentence's primary verb?

It may be a concern of emphasis that Das is placed before the ich in your example.

Also your doubts of Yoda Speech don't really apply, in German translations it would be rather

"Konnte nicht tun ich das."

You could as well say

"Ich konnte das nicht tun."

instead of

"Das konnte ich nicht tun."

which counts against your argument (emphasis mine)

As a native English speaker myself, in comparison with German, English appears to be much more "Speaker centric" ... .

I have noticed this pattern for a long time, but as of now, I still have failed to come up with a pattern I could remember that would guide me as to when and where I should put certain sentence elements on the two sides of the primary verb.

Können is an auxiliary verb in that sentence. The primary verb is tun.

The verb always appears at the second position as @CarstenS mentioned in their comment.

You can check this at the link https://en.wikipedia.org/wiki/V2_word_order .

Can someone explain how German speakers think about sentence elements in a way that tells me where I should put the main sentence elements? Most notably, the two primary actors that reside on the left and right side of a sentence's primary verb?

It may be a concern of emphasis that Das is placed before the ich in your example.

Also your doubts of Yoda Speech don't really apply, in German translations it would be rather

"Nicht tun konnte ich das."

As mentioned in my comment, you could as well say

"Ich konnte das nicht tun."

instead of

"Das konnte ich nicht tun."

which counts against your argument (emphasis mine)

As a native English speaker myself, in comparison with German, English appears to be much more "Speaker centric" ... .

The verb always appears at the second position as @CarstenS mentioned in their comment.

You can check this at the link https://en.wikipedia.org/wiki/V2_word_order .

It may be a concern of emphasis that Das is placed before the ich in your example.

Also your doubts of Yoda Speech don't really apply, in German translations they would be rather

"Das ich konnte nicht tun."

or

"Konnte nicht tun ich das."

You could as well say

"Ich konnte das nicht tun."

instead of

"Das konnte ich nicht tun."

which counts against your argument (emphasis mine)

As a native English speaker myself, in comparison with German, English appears to be much more "Speaker centric" ... .

I have noticed this pattern for a long time, but as of now, I still have failed to come up with a pattern I could remember that would guide me as to when and where I should put certain sentence elements on the two sides of the primary verb.

Können is an auxiliary verb in that sentence. The primary verb is tun.

The verb always appears at the second position as @CarstenS mentioned in their comment.

You can check this at the link https://en.wikipedia.org/wiki/V2_word_order .

Can someone explain how German speakers think about sentence elements in a way that tells me where I should put the main sentence elements? Most notably, the two primary actors that reside on the left and right side of a sentence's primary verb?

It may be a concern of emphasis that Das is placed before the ich in your example.

Also your doubts of Yoda Speech don't really apply, in German translations it would be rather

"Konnte nicht tun ich das."