A couple of points..
The switches now sold are from off-shore, and of varying quality.
If possible try and source a Mopar OE one.
I have a collection of (5) different A-833 back-up light switches,
some work fine others are questionable. I also note that some
require a
slightly longer throw or push to activate..When I had the same problem with the back-up light circuit in my 70 RR,
I took out my multi-meter and did some continuity tests noting the amount of travel required
and ended up installling the one that had
the shortest travel..Just my $0.02...