Familiarize yourself with expressions. Nothing fancy, just the simple pickwhip variety. You can then connect effect controls to otehr properties, e.g. in your case the bulge center to the looking glass position.
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See this page:
I encourage you to use the After Effects Community Help search. The page that I linked to and several others that answer your question come up when I search for the words in your question.
Thanks. Worked perfectly.
Thanks for providing the link.
As to the Search function, I usually do try to search first because I understand these forums are pretty much run by volunteers who are giving freely of their time and expertise. That said, I rarely find what I need. Probably has to do with how the info is indexed, plus my overall lack of familiarity with After Effects at this point. For instance, I just tried putting in "linking a layer to an effect on another layer" or something like that. That pulled up a list of 20 or so items. There were a couple of links to Expressions, and that probably would have tipped me off to the right answer.
Anyway, I appreciate the link you provided, and I'll try to work on my searches.