Because there are no schematics for Rev D where CN181 EXT BAT connector is visible I don't know if it will recharge its internal battery or external battery connected to CN181 EXT BAT. Does anyone know this?
I already tried SAFT LS14250 3.6V Li-SOCl2 and it seems to keep time and date, but this battery type is not rechargeable and all recharging operations to it are forbidden, so how can I check if recharging current comes to CN181 EXT BAT or not?
Easy to check; simply connect a voltmeter to the outer two pins of the external battery connector. If you measure next to nothing while the computer is powered on, it means the computer will not supply charging current to the external battery connector.
Anyway, I'm fairly sure the A4000cr RTC circuit is nearly identical to the A4000T RTC circuit. See the nasty scan of my tatty schematic sheet
here. The external battery connector (CN180) is designed to connect directly to a T1AA/C lithium battery. These are still commonly available from electronic parts wholesalers such as Element14, RS, DigiKey and some computer parts stores may stock them. Google will find a source for you. This should be fine for the A4000cr as well.