Depends on what serves the tune best. Sometimes I'll stick to pounding it out straight, othertimes I'll cut loose, and all points in between really.
Really depends. Sometimes I have to cover for an inadequate second guitar player so I have to keep it simple. Other times I go crazy.
In a rock setting i would try to hold down the rhythm and harmonic progression to make the guitarist sound good. Might throw in some fills if i think it could add anything to the feel. In jazz, i would probably be playing variations over the chord progression, but keep a solid rhythm, walking or otherwise. But obviously it all depends on the music being played..no hard rules.
I improvise at all points during a piece of music. But realize that "improvise" does not mean "solo" or "overplay;" it simply means there is not a set line to play. Certainly there are times when an established line needs to played, but I generally prefer to create a line on the spot that fits the tune. As for what I do when a soloist is taking a solo, yes, I generally tend to improvise more, or further from the core of the tune. However, I don't just listen to the soloist, I listen to the whole band. In my experience, building to a crescendo during an instrumental solo is best effected by establishing a pattern early on in the solo and then pulling in the percussion by playing a descending line (often syncopated) over four or even eight bars that really stands out from the previously-established groove. If you have an attentive drummer (my band has two), you can really lift the whole band by ending that descending line with a double or triple stop. If it works, then the whole band is now boiling and you can just ride the wave. The energy of the soloist now determines how long the energy will last and you can slide back into a chorus, verse, or other interlude, thereby utilizing dynamics in both high and low configurations.
We are original so there are no tabs to follow. That being said the guitar solo usually goes over a verse, chorus, or bridge pattern. I will usually take advantage of this chance to somewhat modify what I play. Sometimes it is utilitarian to "fill the gap" of the missing regular guitar part, sometimes it's just to be creative. Sometimes I use it to try out new variations of the lines. Throw in an octave pattern, add a run or a fill, or try to quietly recreate the vocal lines.
Depends on the song really; sometimes it's best to be tasteful, lay back and not step on the guitar part, other times everyone in the band goes mental.
By "use tab", are you asking about doing this while practicing? When practicing, anything goes unless you're practicing with others and it's more of a rehearsal. If you're practicing alone, play any time you want- it makes improv easier and it also improves ability during call and response sections. If this isn't about during practice, there's a time for bass soloing (or drums, keyboards, horns, etc) and during someone else's solo isn't that time. If everyone solos at the same time, it's just not going to sound good because nobody is establishing a rhythmic or harmonic foundation and there's no way to know what anyone else will be playing, so there's no way to know what to play that works with what they'll play in the later bars of the song. If anyone not serving the song, they need to do something else unless they're so good/adored that nobody cares if they just noodle around.
I have to add that i have a keyboard player in the band so I'm free to play what I want during solos since the keys are playing much of the low end. Listen to Rush doing a cover of Crossroads to hear bass and guitar soloing together.
I like to pick a groove during someone else's solo. If there are more than one solo on a tune (e.g. one of my recent arrangements has a cello solo and then moves over to the synth player), the drummer and I had a different pattern to play underneath each soloist. This keeps the band together, but offers some architecture to the song. Then, the original groove comes back, and the tune could simplify to the end.
recently been playing devo/servotron type stuff over the solos, because it contrasts well with the extreme japanese noise metal solos our guitarist does, and i'm being completely serious not trying to be a smart a
I grew up playing in 60's-70's power trios, so I got used to being more active during the guitar solo so it wasn't so empty. I still do that now to an extent, depending on the song.
we are currently booking fall shows at art fairs, alternative spaces, and little museums, so i'll shoot everybody some live stuff via youtube eventually
A solo does not have to be improvised, on the contrary, the best ones are well designed and practiced in advance.