No battery survives 4 decades, more so if it was even only sold to last a few years (4). The problem is, that while 6 V 1.6 Ah battery packs still exist, I couldn't source any that would have fit into the place as EA-50B did. The ones I found were all slightly too high. Also none of the batteries I found had the connector Sharp used.
Since I would need to come up with new solution, I decided to use LiFePo4 cells as they can be used as a drop in replacement for Pb batteries. 2 LiFePo4 replace 3 Pb cells and the charging characteristic is similar enough in theory to allow the replacement to be charged with the old circuit.
I could not source the AMP connector used within the EA-50B and since the old battery was dead, I opened it carefully and removed the connector to use it later. Hints about the connector type would be much appreciated, as other collectors may haven't a spare battery to disassembly.
There are two options to charge the LiFePo4 cells: use an external charger or charge them in place. The external charger is the easiest solution, as I'd only have to add a Schottky diode to stop the charging current. The in place charging need more care but would make the replacement battery pack a real one. In both cases a case is needed (no pun intented) so I ordered one big enouch to take the 2 LiFePo4 cells (size 18650) but also a battery management system (2S 8A 6.4V LiFePo4 BMS Protection Board).
At the moment I'm waiting for the cells to be delivered and then I can test, if the existing charging circuit works with the MBS or if I have to go back to the diode solution.