Get one of the new rectifiers that use Mosfets instead of the standard silicone diodes.
As a 2000 model, your Aluminium electrolytic reservoir and filter capacitors are now 23 years old and they work really hard because of the pulsed DC that hammers them. Electrolytic caps begin to leak DC after a decade (give or take) depending on the climate, hours used, equivelant series resistance (ESR) and build quality.
Capacitors are the main failure point in a rectification circuit (AC to DC) and usually fail to short. When a battery is connected, they drop voltage because it's drawing more current as voltage is proportional to current.
The heat produced by the OEM rectifier doesn't help its health either. If you get a new one,
maybe reloate it here.
Some of the better aftermarket rectifiers use more effective heatsinks and better bridge rectifiers. They run cooler, are more efficient and will have new capacitors. It's certainly due for a new one.
Working in the electronics industry, I know that any appliance will only last as long as the roll of the dice because there are too many variables to contend with that can predict the life of a passive component. Anyone with a 24 year old rectifier that swears it's still going great is living on borrowed time lol.
I just fixed a friend's living room 7.1 surround sound amplifier, and sure enough it was the rectifier power board. Always the first to go especially with those cheap flat screen TV's. The TV's are always fine! It's the filter caps that clap out. $10 later and it's good as gold. Repair men won't tell you that though.