(Tested for Vanilla 1.21.1)

The time it takes for a comparator to activate/light up after an item has been placed inside of a hopper minecart it is looking at is random. From my non-exhaustive tests, I have seen a time range from 3 to 22 ticks pass between the time the item is placed inside and the comparator lights up. The time it takes is not location-based.

Steps to reproduce:

1) put up some minecarts on detector rails (in vanilla minecraft, only detector rails work, as far as I know that's intended behaviour)
2) place comparators that are observing the contents of the minecarts
3) input the command /tick freeze
4) put an item into each of the minecarts
5) repeat the command  "/tick step 1t" until they light up, this way it's obvious that they light up at different times
6) Repeat to see that it's not based on location