I read this post:
https://www.eevblog.com/forum/testgear/fluke-732b-repair/ . I followed it: replaced R520 with a 16.5 Ohm, added C541, and I replaced U501 and Q502 as per the manual section on the charge circuit.
I have constructed an oven-thermistor and battery-voltage-monitor cable that connects to the D-sub 9-pin on the rear of the unit. It's not official that one can monitor the battery voltage by connecting to the ext. bat. in pins, but I checked it against the voltage at the battery terminals, and it's accurate to within about 200mV.
If I discharge the battery to a point at which the constant-current charger stays on (charge LED is lit), it won't switch to trickle charge, even at over 16VDC at the battery (after 48 hr. charge). And 'it is' stuck on constant current. The charge light is not in error.
But, if I cycle the AC power, the charge light is lit for several moments and goes out, as is normal.
So, the charge LED is accurately portraying the charge type (it goes out when the unit switches from constant current to trickle charge). I just don't know why the charger won't switch over to trickle charge if I just leave the unit plugged in to AC.
What could make it work only when the AC power is cycled?