Mute like the master

Other than his fantastic feel, technique and overall creativity (and super-dead flatwound La Bella strings), one of the key elements of James Jamerson's bass playing is the sound he got from his '62 Precision - in particular, the clarity and controlled separation of each note.  One source of this sound characteristic is intrinsic in the unmodified, stock 1962 Precision bass - the bridge cover that contained a string mute.

At some point in the 60s too many players were removing these mute/covers, which resulted in Fender modifying their standard to exclude the cover - with the result being that each string continued to ring for a long time, and took the sound of the bass guitar even further from the upright doghouse bass.

Other than Fender basses with their bridge covers intact, I've only played one other bass that incorporated string muting - the 1980s Music Man Cutlass I (which was essentially a limited edition Sting Ray with a Modulus graphite neck --- man I wish I still had that bass). Amazingly enough, this great bass had individual sponges under each string that you could individually adjust for variable degrees of muting by string (using a screw mechanism much like a fine tuner).

So beyond the technical aspects of the playing itself, the James Jamerson feel and sound can be difficult to come by.

BUT ...

As a workaround, you can do what I've done, which simulates the original string muting of the '62 Fender and gives you a foundation sound to work with for 60s soul and R & B:  cut a small strip from a kitchen sponge (about 1/2" wide - and obviously you'll want to choose a sponge with a color complementary to your bass) and slide it underneath the strings right next to the bridge.  It will compress just enough to mute your strings, and you can easily slide it out when you want to return to a ringing tone.

There you go.