Welcome to the JD
forum of GTTalk. You are correct. The 312 should have rubber mounts. The bad news is that they are expensive. From JD
they are about 30$ each for the rear and 50$ ea for the front. You may be able to find good used ones or find an alternate source for them. I have heard of sellers on EBay. I just replaced the 2 rear ones on my 314 which is very much like a 312. You can get access to all the parts diagrams for your tractor by going to jdparts.com and under model search put in 312. This will bring up a list of models with 312 in the name. Select the 312/314 garden tractor and then the sectional index. The motor mounts are in the Frame diagram. There is a sticky or a thread prepared by one of our members on using JDparts but I can't recall just where it is. One other thing to check is the driveshaft couplers. If the PO let the tractor run with bad mounts for an extended period of time the vibration can cause the couplers to wear at both the engine end and at the hydro. Give this a good close inspection. On my 314 the engine coupler was very worn, The keyway was nearly stripped out. The parts are still available from JD
. Good luck with getting it sorted out.