I have a GE Smart Home low voltage switching system in my 1955 home. My transformer (120vac/24vac 40va) keeps blowing and I have since read that I should add an inline fuse to the 24v side to avoid blowing the transformer. My question is, how do I find the short? There are many low voltage wires coming to the secondary terminals and they are all wire tied together. When I place a meter to the ends I get zero. When I connect the transformer I get 9-10 v at the secondary terminals, it heats up quickly and blows after 2-3 minutes.

Do you have pushbuttons for switching latching relays? If so, you need to measure the resistance of each of the relays coils, one may be shorted.

Some have a separate wire to switch off, a dual coil relay, and it will have 3 wires for control instead of 2.