Are there any general rules that indicate when the plural of a neuter word is "-e" or "-er"?
I haven't found any rule for whether neuter nouns built on a monosyllabic root (that is, nouns that are monosyllabic if we ignore prefixes like ge-, or compounding as in Bergland) in the singular pluralize in -e vs. -er.
I think that -er is less frequent than -e
My understanding (I'm not completely sure) is that -e is more frequent and also generally more productive than -er.
In all three frequency lists used in the present study and also according to Bittner and Köpcke (1999) –s, umlaut, and –er have a low frequency. Clahsen et al. (1995) did not consider umlaut as a part of the plural system, but –s and –er reached low percentage values in all three frequency lists they analyzed (types and tokens).
(p. 107, "Influence of intra- and extralinguistic factors on the distribution of plural allomorphs in German", by Eugen Zaretsky and Benjamin P. Lange, in California Linguistic Notes Vol 39(1) Fall 2014. Bolding added by me.)
Part of the reason for the overall low frequency of -er would be its restriction to non-feminine nouns, but even when we exclude feminine nouns I think -er is not quite as common as -e as a plural ending in German. The relative type frequency of -er vs. -e for neuter plural nouns will depend on the word list. I don't know the details of how -er and -e nouns differ in overall frequency or in other respects. Zaretsky and Lange say that out of the 1000 most frequent neuter nouns in the Corpus of the Leipzig University (p. 79), 62% have plurals in -e, followed by 18% with plurals in –er (p. 108).
Unfortunately, there are many parts of Zaretsky and Lange's results that I don't understand. For example, one of the three corpora that they looked at consisted of the "500 most frequent word forms (tokens) for each of six plural allomorphs according to the [Corpus of the Leipzig University]" (p. 79): I don't understand how one could get useful information about the relative frequencies of plural-formation strategies within a single gender from such a corpus, but for some reason Zaretsky and Lange still treat that as a meaningful percentage, which confuses me. You can look at the paper yourself to see if the other results make sense to you.
There doesn't seem to be a rule for when to use -er
The following two papers that I found online discuss parts of the rules for German plurals in some detail, but don't give a rule for when -er occurs (either for masculine or for neuter nouns); they only note that in the plurals formed with -er, umlaut (for nouns that contain back vowels in the singular) is usual:
In no case can it be predicted whether an umlauting [−fem] noun belongs to [the class of (nonfeminine) nouns that have /r/ in the plural] or not.
(p. 5, "German noun plural reconsidered", Dieter Wunderlich, University of Düsseldorf, April 1999 - still incomplete)
the suffix –er, [...] attaches to a lexicalised class of monosyllabic nouns only
(p. 8, "The grammar and typology of plural noun inflection in varieties of German," Richard Wiese)
The only thing I can guess might make a difference to the use of plural -e vs. -er is a word's status as a Fremdwort. Neuter Fremdwörter can pluralize in various ways (with -e, but also with -s, as in Restaurants, or -en, as in Partizipien), but I don't currently know of any word in this category that takes an -er plural. (A side note: Wunderlich says on p. 12 that there is variability between -e and -s plurals for some speakers with some words.)
Many such words are built on a root that is more than one syllable long, so I think that could be an alternative criterion for excluding the possibility of an -er plural. But I don't think this is a very useful rule, even if it is accurate.