Jamerson used the floating thumb,?

no

 

No one really invented it, but some are linked to it because they popularized it.

 

what he did was rest his fingers on the pickup cover, so technically suppose it is a 'floating thumb' but i dont think he intended it to be about that.

 

it floated, but he didn't use it for muting or anything like "real" floating thumb users.
jamerson used only his index finger and I believe he muted with foam under the bridge.

 

I recall in the videos I saw of his technique, he anchored his little finger on the Pickup ashtray and plucked with his index finger.

The way Fender designed the Precision, you were supposed to anchor the fingers of your right hand on the "Tug Bar" below the G string and pluck with your thumb. The Pickup cover was there to keep your sleeve and forearm from catching the strings.

The bridge ashtray on a P had a foam mute glued to it as standard back in those days.

 

He definitely used the floating thumb to mute strings, but not in the way most do these days, namely resting the thumb on the string lower than the one being sounded.

Instead he let his thumb hang straight down over and against those strings, and I suppose he muted strings higher than those being sounded with his LH.

You can see this clearly on the few minutes of footage around of him playing, and if you try to play the way he did with your index finger only, this thumb muting technique feels very natural and logical.

The bridge mute he used was standard for the era and reduced sustain and overtones, making for a fat, pulsing thumpy tone. It's a gorgeous sound with flatwounds.