Tony,
I think your accordion background contributes to a lot of your (and other players too) rhythm and timimg capabilities.

If you take a minute to think of whats going on in each measure of a song that you play on the accordion, you can't help but to increase your rhythm and timing functions.

Left + right hands are playing 2 different things, but there's no sound, no music without physically pushing/pulling the bellows back and forth.
So you simultaneously maintain that control (in timing/rhythm) the positioning of the bellows, otherwise the volume level is too loud or too soft, OR, no sound at all because you just ran the bellows shut.

After you have developed that coordination (timing/rhythm) you work on accenting your music. Again, 2 different parts being played at the same time with only 1 source of accent control, the bellows.
Your rhythm develops to a higher level thru this training because you develop techniques to get your fingers off the treble keys for a split moment so you can accent a bass passage and vice versa.
The hand learns to become quicker than the ear (of the listener)

After playing a few years, this becomes automatic, mechanical without thinking about it.

Hence, rhythm and timing thru training.