Can anyone tell what may be the problem when the fuel gauge reads full all the time?

Thanks

1987 what car truck? anyway you checked all fuses in car and under hood? usually it means bad ground. but you need to what you got like i said.

You're probably gonna' have to pull the pump / sending unit, to test the float arm.

It can be pulled withOUT removing the tank. No special tools needed, except torx drive sockets for the filler neck bracket.