I would have said, purely based off of guitar playing, John Lennon. His guitar playing wasn’t flashy, but it seemed like it was the glue, musically. It was the rug; it really tied the room together.
If Lennon is not within the parameters of the OP, then Jason Newstead. Bass player for Metallica during one of their most popular eras. Some of the purists would say that Cliff Burton was the better bass player, and they may be right. But Newstead is when they had their biggest mainstream success.
Terribly underrated. He brought so much to that signature sound, both with the bass and his backing vocals.
My brother was once working site safety backstage at an AC/DC concert and Angus’s wife Ellen spent some time chatting with him. She said that she and Angus spent most of their time in Holland where Angus was happy to be famous locally as the postmaster’s daughter’s husband.
I’m going to go with Jazzy Jeff. Still held the the highest regard by pretty much everyone. Will Smith can go be a cartoon, and good for him, but I’m good just doing my thing back here.
If we’re talking utterly vestigal members of a band, how about Andy Fletcher of Depeche Mode? In his 30+ years with the band, he hasn’t written a song. And his singing and instrumentation are strictly background work. Even he doesn’t really seem to know what he does in the band.
Or one of the Vandellas.
Ooh, how about that guy in the Bosstones that just dances?
Ben Carr! There was also Bez, from the Happy Mondays, who did that, although he sometimes also had a couple of maracas in his hand, so I suppose he could be loosely termed a percussionist as well. 
Plus he has name recognition, so he might be out as just “the other guy.” He’s Bez.
Can I be Richard Carpenter while also not being Karen’s brother? Just like me, they long to be, close to you.
For the win!
Thanks for your comment, WordMan. It inspired me to go to Youtube and play Misty Mountain Hop, which I hadn’t heard in quite a long time. I found a video of Led Zeppelin playing it at Madison Square Garden in 1973 and one of the commenters was blown away that Jones was playing the bass line with his feet on the pedals while playing the keyboard groove with his hands. Sounds almost impossibly amazing to this non-musician, especially considering the quality of musicianship those guys brought to bear on their songs.
Ah, a church/pipe organist! Here’s some fun for fancy footwork. (I don’t know this performer–just wanted to find an example of pipe organ that shows the pedalwork that can be involved.)
Huh, I did not know this, but apparently, he did play organ in church.
Wow! That organist was amazing!
Thanks for the link and the comments from JPJ. Makes more sense now.
Hall gave Oates writing credits on all of their songs. Oates, in his own words (paraphrasing) I am the best paid backing vocalist in history.
And he got to work with Handsome Boy Modeling School too!
Waddy Wachtel, perhaps. Waddy Wachtel was ‘that other guy’ in about a million songs by a dozen bands. He’s played with Fleetwood Mac, Warren Zevon, Joe Walsh, James Taylor, Tom Waits, The Rolling Stones, among many others. He’s also done movie work and production. But no one knows him.
He also co-wrote 'Things to Do in Denver when You’re Dead" with Zevon. That gets him an extra half star.
No question in my mind…Alex Lifeson.
Peart was always recognized as the quintessential drummer, and Geddy is the frontman, but Alex is what really sets Rush apart, and he’s like the forgotten bandmember. He’s also a guitar hero of mine. 
Yeah, yeah, yeah. You just want Andrea. 
Yep, I saw The Boys From County Clare too.
I’ve been in lust with Andrea Corr since “Talk On Corners.” Easily one of the most beautiful women I have ever seen. And she married a billionaire.
All three at the same time!
Actually my favourite is Caroline, the drummer.
Excellent choice! Great player who has been everywhere and played with everyone. Here’s a link to a recent thread in the acoustic guitar forum featuring a link to an interview: interesting article/interview with Waddy Wachtel - The Acoustic Guitar Forum
I love the fact that he doesn’t use effects. My kinda guy 