Due to the age, I'd have to look through some old service manuals to see if I have any info on that furnace. Due to this, I cannot say for sure whether that is all that is needed to be done.
However, it does sound fairly accurate without any furnace data or pics.
Because it could be a bad gas valve also, I would have the gas valve inspected and checked first before going to all that trouble.
Does the pilot light while holding button or knob, then go out when button/knob is released ?
Or, does it do fine, but go out in a short time ?
Some people are Humbly Grateful, while some are Grumbly Hateful.................... Which one are you ?