65 sounds okay to me. Changing points is really pretty easy. I've done it on three very old briggs motors that did not run at first, and every one has worked great afterward. The condensors are what fails, usually the points are still okay. But I change the whole mess since you are in there and the parts are stupid cheap.
Pull the recoil starter/blower housing off first. Getting the flywheel attaching nut off next - is the toughest part. If its an old briggs and uses the old style ball bearing starter - I've found that a large pipe wrench and a big screw driver set across the cooling fins on the flywheel to stop it turning works fine, be gentle. Just be careful not to bust the flywheel cooling fins. Give the flywheel a sharp tap on the backside and it should pop off. Point gap is to be set at .020" on most of them. Take your time setting the gap and make sure its right, check check and double check once tightened down, the gap will change a little when you tighten the condensor down. You might want to clean rust off the flywheel magnet and the coil areas where they pass each other. A little fine steel wool works nice, remove any bits of steel wool after you are done.
Bet it runs like a top when you get it back together.