Furnace is a 1976 forced-air natural gas furnace. I've been doing maintenance on it, but found myself caught up with wondering two things about the 24V transformer: 1) where are the leads for the transformer; and 2) are the taps just screws jammed into the secondary?

Looks like the primary are the 2 soldered wires. Measure AC across them to check. Some older units are mounted on a metal box and the primary is on the back side. This is a heat only stat? The screws are threaded through the red board.

That transformer appears to be a "fan center" which would also bring on the fan if you had A/C. It also would supply 24 volts to the oudoor unit & provide a connection point (Y & C terminals) for the outdoor unit.

Primary must be on the other side. The 120V primary supply is coming from the j-box to which the transformer is mounted. The voltage across C-G is 0v; across C-R, 24V; and across G-R, 24V. What is the G terminal then? Is it a fan terminal? If so, what is the terminal connected to inside the transformer?

'G' is the fan terminal. Circuit closure between R & G should bring on the fan if the relay is so wired.

'G' is the fan terminal. Circuit closure between R & G should bring on the fan if the relay is so wired.
Thank you for pointing out that the transformer belonged to a combination transformer/relay unit called a fan center. However, no one I've spoken to or questioned online could explain why 0V was read across C-G but not G-R and C-R, except to say that 24V would be read only when the fan was running. This is not an explanation. It does not explain what's going on inside the transformer. Finally, I found schematics that show the operation of the fan center, which I would never have found without the words "fan center". Thank you for that. For some reason, no search at Honeywell etc. for transformers produced results for a fan center. How stupid.

http://www.cgnacontrols.com/members/product_documentation/60203a973aa360af_cat_pg_.pdf

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The reason there is no voltage G-C is G is a load terminal. If voltage is applied to G via closure of R-G on the stat (if it were so wired), the relay would operate. Think of G as a place to receive voltage.