1984 Chrysler New Yorker Reverse Lights not working

Double and triple check the fuse for your rurn signals both visually and with ammeter to check for fuse continuity, or just replace with new one of same amperage. The fuse can look good but have a hairline crack that is not visible.

If bulbs are good then you need to check the switch that powers them when you put the car into reverse.

FYI - Neutral safety switch prevents car from starting unless it is in neutral transmission position only.

You have a direct short. Take the bulb out of dome light, inspect the socket. Try putting fuse back in while bulb is out. If the fuse blows again, Id say it's in the wiring from the fuse box to the the switch. If the dome light fuse also covers other electrical things, such as lighter, check the socket at all points. You mentioned that other fuses were replaced as well? Which ones, and why did they blow? Sometimes it could be moisture entering your fuse box, or condensation near the computer, but is sounds more like a short. Could be as minor a a bad ground wire, or a chafed wire. While you are putting the fuse back in, it will help to keep your eyes looking around the fuse box for sparks as soon as the fuse goes in. You should also listen for that electrical snap. If this doesn't help, I'd suggest taking head panel down and follow and inspect the wires from dome down to the switch. Then from switch [ which could also be the cause ] to fuse box. look for hot spots, arcs, and bare spots. I hope this helps you out. keep me informed

My guess would be the neutral safety switch on the transmission.
The switch also acts as a backup light switch when the shifter is in reverse.
I would check for power at the switch for the reverse light circuit.

okay if the light work then it wont be a fuse, this sounds like a bad connection or bad cluster. remove the cluster and unplug the connectors to it and then reconnect them and start the car and see if they work if not then i would say the cluster went bad, good day.

check bulbs/ fuse/ reverse switch on gear box/broken wire

Check the stop light switch down by the brake pedal. there's 2 wires going to the switch. when the pedal is pressed the little button on the switch comes out and causes the brake lights to come on. Try unplugging it and putting a jumper wire in the plug to complete the circuit. Second guess: if the car is rusted, check the wires in the trunk above the wheels.

There are 2 switches on the transmission,one is a nuetral safety switch and the other for the reverse lights,but there may possibly be a relay involved with the reverse lights also.

You may need to go back and check the bulbs again,,, because if it's using a standard 1157 bulb, the bulb plugs in "only one way",,, but is easy to get installed incorrectly,,, causing a short which blows the fuse.
If you find this not to b the case,,, then remove the emergency flasher switch from the fuse box along with all the light bulbs, front and back. Then reinstall a new fuse.
If it still blows the fuse without bulbs in it, the you either have a faulty bulb seat or a wire is pinched and grounded to the body somewhere. (this will require an intense visual inspection)

I have had this happen and it is rare, but I have had a filiment burn out in a two filment buld and short to the other filiment. It does happen and I think this might be your problem, the only way to find it is a visual inspection of each bulb. I am sure many people will think this is crazy, but I have had the exact same problem, I had the schematics, tested the circuits,etc. and them by accident found a stop/blinker 1157 bulb that had done this exact thing. I hope this helps you, check the bulbs in your headlights also.