Funny thing about a good bass guitar sound... and this is my personal experience but I rather think it travels well.
First and foremost, yes Carol played a Fender Precision for Brian Wilson and yes, it was a lovely tone to be sure. Now, also consider Sting from The Police. He also plays a Fender Precision and did so on all the The Police recordings.
Consider this fascinating aspect about a good bass guitar sound. Even on a shitty little transistor radio with zero bass freq response we can still hear that gorgeous bass guitar riff to "Good Vibrations" or the lovely staccato riff played by Sting on "
Roxanne".
Most people think that bass guitar is supposed to be precisely that - booming low frequencies so low they'll shake the house. Sorry, wrong answer. Such earth shaking sounds are actually the job of your kick drum and floor toms.
The job of Bass Guitar is to hold and sustain the root note, and or similarly important notes to the melody which is being played in concert with it at that time. Singularly, the greatest defining aspect to a good bass guitar sound is 'sustain' - that is, the ability for a note to hover without decaying off into silence. Next, after that, the most important aspect is just plain mid range tone around 500-800 hz. Believe it or not, it is THOSE frequencies which we're hearing most of the time in a song - and it's THOSE frequencies which are signalling to our ears "Hey there's some serious bass going on here which you could hear if you had the decent speakers dude!"
Guitars are quite different beasts - they are laden with harmonc nodes throught the length of their strings. Just by choosing a different plectrum position on the string adjusts the tone of what you're hearing.
Conversely, bass guitar is about holding that one 'pure' note with little or no overlaying harmonics.
So, in closing, the secrets to good bass playing are this... a really tight drummer with a great kick work. The kick drum almost always should play in concert with the bass guitarist. Timing is everything. As a bass player, the closer your timing with your kick drum, the more 'killer' you sound. Next, lots of sustain. Go thu a compressor if need be. Your notes should not drop by more than 3 db over a two second period with just one note I find. Lastly, just dial in those mid range freqs guys. Try upping your freq over 1.0Q by 6db between 500 and 800Hz. If you factor in everything I just mentioned above, by and large, you'll be able to sound like any bass player in history. (Within reason of course... I recognise there are some million notes per second freaks out there but they don't do much for my musical ear sadly).
Remember, rare indeed is the bass guitarist who sounded good without a killer drummer. Follow that golden rule I mentioned earlier and you'll kick a goal everytime. The kick drum and your bass notes are siamese twins separated at birth but they should do everything together in perfect timing.
That being said, now go back to Pet Sounds and have a listen to how good the drumming was and you'll see what I mean. You'll find the kick drum was actually quite loud for it's day and it was no accident that Brian Wilson made a point of forbidding Dennis Wilson from playing on the record. Brian's tunes by that stage had FAR surpassed Dennis's abilities. Indeed, if you ever see any Beach Boys video's of Good Vibrations it's just plain embarassing how out of time Dennis is playing even though he's just miming.