No, the problem isn't an earth (ground) problem in the dash. The lights aren't grounded in the steel of the dash. They sit in a plastic housing, and are grounded through the wiring harness.
But that is a tell tale sign that you have a ground problem at 1 or more of the lights. The reason that you are having both lights light up on the dash is from feed back through the harness.
The most common lights to have problems are the tail lights. They are grounded by the mounting hardware into the body, fronts are grounded through the wiring harness.
Turn the key on, and then select either left or right turn signal, then get out and look at the front and the rear of the Jeep, you are looking for a dim light or a non blinking light. That will be where the problem is.
Pull the bulb and look for corrosion in the socket. Sometimes it cam be cleaned and other times the socket needs replaced.
'87 YJ, 4.2L built and bored, 8.5" of lift, 8.8 rear, AX15/NP 231, Tom Woods drive shafts, Flat fenders, 12,000LB winch, Custom bumpers, Rattle can paint job. Never completed...