For both nouns there is a similar pronunciation of "-ei-" in standard German:
When people in some southern German regions try to speak non-dialect German the pronunciation of "-ei-" is different for "Zeile" ([ˈʦeɪ̯lə]] only but not for "Zeiger" which is likely to be pronounced according to standard German. I can speak mainly for Swabian dialects but some other regions may pronounce this similarly (see "Zeile" in Wiktionary for Austria)
Many other words (e.g. Eis, Weiß (color), beißen [eɪ̯] vs. Bein, weiß (wissen), Reim [aɪ̯]) also show this phenomenon.
Is there any explanation for this?