Strabo said
My experience with mandolin gives me a sense of comfort with chords, double stops and drones in the fiddle-friendly keys that I play. I don’t know much about complex harmonies, but the basic chords seem to fall easily under my fingers. In fact, I do best when I don’t think too much about it. 

I learn mainly by ear, and I have had good success picking up new tunes from videos, other recordings and live performances. Now I want to extend that to playing backup. 

I’m looking for interesting examples of fiddlers supporting others in ways that enhance the overall effort. Right now I don’t know how exactly to direct that search, but I’m confident that I’ll figure something out. 

...my take:

I think an awful lot depends on how well you know a style of music & who you are playing with. 

If you are familiar with the group, ask if they have a general playlist you can audit, take note of what's played & ask what was played at the previous session, if you didn't attend.  The playlist may be too large to memorize, but at least find time to play through as many as possible - just for familiarity (better than nothing).  Ask if there are favorite 'group' keys.

I think after playing with one group for a while it will feel natural to add a few extended chord notes, or lower octave melody notes, to the chords you've been playing for backup.  It couldn't hurt to ask what others in the group want & offer ideas you might have/want to try. 

I do think it's important to stay out of the range of the melody when playing back up.  I like playing lower, but if the majority of the melody is low - you don't have any choice but to play higher backup.  Think I'd be more mindful of dynamics since higher pitches can be piercing.

If new to a group, I'd ask for key & preferred cord progression.  In the related Harmony Thread you indicated a good understanding of what you are up against & the importance of rhythm. 

- If I focus too exclusively on my notes, intonation etc, I can fall out of the rhythm. This is not good, not good at all. Keeping time is more important than good or bad notes. Another Miles Davis quote: “Time isn’t the main thing. It’s the only thing." 

For being supportive, I'd go a step further to focus on the 'groove', once established.  So, even if you only play the chord root, you can experiment with different shuffle bowings - but try to strengthen that established pulse.  Fiddlershop carries the "Strum Bowing" Books by Tracy Silverman - who also has lessons available. 

If you do know a tune really well, you can add some 'in-between' (non-chord notes) while backing, but I'd still stay away from the melody range.

You obviously have the best creative options if you are THE ONLY ONE providing backing. 

SharonC talked about (also in the Harmony Thread) using the "Basic Fiddlers Philharmonic" Books - they provide notated backing you can start with.  There's a book for Celtic & Old-time. 

Basic Fiddlers Philharmonic Old-Time Fiddle Tunes: Violin, Book & Online Audio (Philharmonic Series) 

@SharonC - 

I know you have mentioned several times that learning duet material is very helpful for learning harmony.  I thought you recommended some Duet Books, but I can't remember what they were... help?  

Zack Kline offered up audio & notation for 4 'Beginner' Duets at Fiddleduets.com - "Go Tell Aunt Rhody", "Britches Full of Stitches", "Dawning of The Day", and "Southwind" .  The duet series unfortunately stopped after these offered, but Zack's Fiddle School site has several duet parts for "Wagoner's Lad" - definitely worth looking at.  AND, check out the Rags he has! 🤗  ...he also offers lessons. 

In my teaching I have noticed there are many places to learn melodies, but few places to learn what to add next. So I began to create duets to show students how to fit behind a melody. There are many ways this can be done, from simple chords to complex countermelodies. The accompaniment parts ended up being the more challenging ones, while the melodies are more simple...that is where beginners will want to start!

I have mentioned (elsewhere) that I like Helen Bell's Fiddle Duets - she also has arrangements for Viola & Cello!  She has a lot to say about what makes a good Duet and some great videos! 

... maybe consider 'Fiddle Hell' will be virtual online in April 2024 - there's always great workshops (I won't miss them them) pertaining to backing and several months to review, afterwards.