My horn, radio and inside lights come on without the key in when it rains hard

Question edited for clarity, 'fuse', unless you light it 'fuze'.Question moved to sub category.

If the radio has an inline fuse, it will be within 82 of the plug at the rear. They are built into the harness. Unlikely because there are three fuses covering audio.

https://fuse-box.info/isuzu/isuzu-trooper-1992-2002-fuses-and-relays

C11 10 (AUDIO[ACC]) MIRROR Audio, Door mirror, Door mirror control SW, Door mirror folding SW, Digital clock, Speaker C12 20 CIGARETTE Cigarette lighter C13 10 ANTI THEFT Anti-theft controller C14 15 STOP A/T CONT Stoplight SW (w/o cruise control), Brake SW (w/cruise control), Rear wheel anti-lock brake controller, Stoplight, Transmission control module, Electronic brake control module, Trailer harness connector, Cruise control unit, A/T shift lock control unit, Lockup off relay C15 20 AUDIO[BJ] Horn, Horn relay, Horn SW, Hazard warning light SW, Flasher unit, Anti-theft horn, Hazard warning light, Audio C15 20 TELEPHONE Telephone C16 10 CLOCK[B] ROOM Digital clock, Audio, Dome light, Map light, Luggage room light, Courtesy light, Door SW (Front, rear, tail gate), Antenna, Anti-theft controller, Key remind SW, Seat belt, Key & light remind buzzer

No radio, no lights, no start = dead battery. Even with key off, lights should come on if battery isn't dead

check for loose dirty battery terminals /dirty loose earth points. This is an indication of incomplete electrical circuit

What year is the vehicle ?

try this- put fuse in- pick area of car- say right near the horns- spray with garden hose- wait for horns to come on- you are looking for a "short" or bare wire- hose will simulate rain- do small areas and when get horn to sound - stop and look at wires in that area for damaged wiring- crushed wires or plugs or a spot where wire has rubbed casing off- then tape area up with electrical tape and continue on till you can not get horn to sound anymore with the water

Depending on the year and make of this car or truck when you turn on the key the system runs a test and if the problem was repaired it will shut light off, if the light remains on then theres a problem. even if you had a scan tool reset the light it will come right back on as soon as the engine is started, this sounds like something got wey and shorted out, the first thing i would check is the fuses and then look around at the bottom of the steering column and check connections for water or rusted terminals,inside the steering wheel is a clock spring that contains wires for horn air bag and other controls if cars has them like cruise or steering wheel radio controls, the part called clock spring is what makes the wheel be able to turn without ripping wires, it like a retractable bunch of wires and sometimes they go bad just from turnning the wheel so often, heres a picture of it, chrysler is famous for problems with this, good day.

most likely check to see if horn relay got wet.

How did you test the relay? The fuses are very hard to see without pulling them so use a fuse puller and check it in good lighting just to make sure.

If it is OK, go to radio shack or harbor freight or any auto parts store. Buy a cheap test light or multimeter and check the wires coming into the horn assembly from the harness.

If your friend honks the horn and the light illuminates, then you know to get a horn from a junk yard or ebay. If the light does not come on, then you have an upstream problem.

Check your neutral safety switch. I had the same problem during a hard rain, hit a bump and everything went out.