In the oldest reliable references from the 1920s, it was a $2 bill, $1 bill, a watch, and a dime.

So keys and contacts are both modern revisions.

I thought I sensed the implicit presence of the Quote Investigator!

https://quoteinvestigator.com/2013/04/11/better-light/

I used the AI, the web, and even tried to verify with full page scans but then I realized I have a job.

Over a century old! https://en.wikipedia.org/wiki/Streetlight_effect

Does the specific object matter in any way at all?

No. For example, in science most scientists just look where the streetlight is, but a small number of people build better, stronger lights to search larger areas, and there is a tiny number of people who can mysteriously just find things in the dark.

I just thought it was weird it was framed as "a skit we did in school" when it's a literally-ancient-old joke.

Contact lens is the way I have always heard the joke.