Another way to approach a two-pickup bass: turn the volume on your dominant pickup down to 8 or 9, then blend in the secondary pickup to taste. That bit of series resistance between the pickups will improve blending capabilities; when both volume pots are wide open, one gets fewer shades of blending, because the wide open one quickly overpowers the one you're turning down.
Cool tip. I'm gonna play around with that some.
Also,,, not to go down a rabbit hole,,, but a comment about amplification, cab choice, etc... When I first got my jazz, I was playing through a rig that was not the best. It was a fine rig, worthy of any gig... not advocating buying "boutique" gear as a fix here. But the cabs were dark sounding, really rolled off at like 4k so no top end, and kind of had some really pronounced low mid frequencies. It was a fine rig, but kind of made everything sound the same. (this is the "transparent" thing folks talk about). At that time, I really couldn't hear a difference when blending pickups.
Later, when I switched to a more transparent, open sounding rig, with more top end, and more even across all frequencies, then all the sudden my ears opened up and I could really hear the smallest changes when blending pickups... A bit of an "ah ha" moment.
If your cabs, or eq, or too much tone shaping are choking off your sound, it can all sound the same and rolling a pickup back a little to cut through for a certain song or other subtle changes can kind of go out the window. There are some cabs, or amps, or PA house systems and room that are not great and just kind of make everything sound like -whatever- no matter what.
Listen to your jazz on it's own (maybe with good headphones) and blend the pickups and listen to the tonal changes. The more your train your ear to hear that stuff, the more you are able to use it when it comes to showtime.