Did this a while ago. Transformer fused in out. Very stable ohms.
More of the LM317 battery replacement
More Eico 232 LM317 REPLACEMENT
I have a slightly older Eico where the previous owner rigged up a substitute for the battery by tapping off the filament winding of the transformer, all he used was some diodes, a resistor, and some large value, low voltage, electrolytics. It worked fine for me until I blew out one of the resistors on the Ohm meter section after I accidentally used to to measure some high voltage.
Regards
Arran