You probably already know but if they are colored ball ends they're D'Addario.
I'd be willing to bet the string modulation is due to a twisted string.
Interesting. I've never heard of that happening. And yes, colored ends in the strings.
Since the seller had scatter-wound the strings on, I loosened them and cut the ends to string them properly pushing the string end into the peg head. Now there's less of that chorus-like modulation.
I have tightened the neck several times now during the time I have had it, there is stil a little room for tightening, I think. The bridge saddles don't bottom out any more and I don't need to adjust the neck angle. I had to screw the pickup down quite a lot due to the clank I got when I lowered the saddles.
It's surprising how bass owners don't realize they actually can have a working instrument with just a little of tweaking and patience.