Just from the photos, I'd say it has seen better days. I mean, c'mon, it's 50 years old. Did you think it wouldn't die of old age eventually? Nothing lasts forever, and that includes RV gas stoves. Rather than throwing good money after bad, I'd recommend replacing it outright. Some things aren't worth throwing money at, and this is one of them. I know that wasn't what you wanted to hear, but it is shot. Time for a new one.
A while back I replaced my Suburban two burner stove, (which wasn't near that old,) but I didn't like the poor performance from it. I replaced it with Dometic stove with recessed mount to the counter. It has sealed burners, piezo electic ignition, and allowed me to cut down a bamboo cutting board to fit in the stovetop recessed area. Easy to clean too. Just lift off the grate and wipe it out. I think it also looks much better as well.
And while I was at, I also replaced the "birdbath" sink with a new 9" deep stainless steel bar sink as well.
And this is the stove I installed, for probably for no more than having a service tech call-out, just to tell you they can't fix it. It's only $250 bucks out the door.
https://pantherrvproducts.com/50216/