I doubt the proximity of the battery has any effect on the reg/rec.
I did the checks on the Honda reg/rec. It has three yellow wires, a red/white, positive to the battery, and a green, negative to ground.
with the red meter probe on the red/white wire the three yellows had these readings.
Yellow #1 was infinity reversed was .591 on the 2k scale
Yellow #2 was infinity reversed was .590 on the 2k scale
Yellow #3 was infinity reversed was .551 on the 2k scale
With the red meter lead to the green wire
#1 was .585, reversed was infinity
#2 was .545, reversed was infinity
#3 was .591, reversed was Infinity
Using the diode checker
Red to red/white I got
#1 was infinity, reversed was .695
#2 was infinity, reversed was .694
#3 was infinity, reversed was .650
With the red to green
#1 was .690, reversed infinity
#2 was .642, reversed infinity
#3 was .689, reversed infinity
The book said the high ohms should be over 2k ohms, infinity is higher than 2k. The low side should be 5-40 ohms. I got .545-.590 on the 2k scale, that should be 545 to 590 ohms. I bit over the 5-40, but I think it's ok.
The difference between the high and low is large enough to prove the diodes are working, no shorts or opens anywhere.
On a PMA with out any load on the system the voltage goes nuts, jumps all over the place. Sometimes it jumps around so much a meter can't read it on the DC scales.
The battery or cap provides the load nessary to stabilize the output voltage.
I think that small a battery will work ok. It may not last long. They aren't designed to take the charge rate of a bikes charging system.
Most lead acid batteries can handle a charge rate 1/10 of the amp hours. If that applies to these tiny batteries I can't say. I have a lead acid 4 amp/hour battery and the charger that came with it is 800 miliamps. Or .8 amps. Which is actaully a bit more than 1/10 of 4 apms, that would be .4 amps. I think on charge rates that low it won't matter as much on the battery size.
Now on the bike the stock system can put out about two amps more than the bike needs to run that is used to charge the battery. Hugh's PMA puts out a bit more and doesn't use some of the output just to run itself so it has about 4-5 amps extra after running the bike to charge a battery.
This 5 amp charge may shorten the life of a tiny battery.
From what I have read the batteries don't cost much so short life is not a big deal. ust something to be aware of.
Leo