Wasn't from the brake pedal. It came from one of the footrests  . I don't know if it was sheer coincidence that the spring popped off or not. Anyway, mystery solved and it's back on.  Also, the bike started back up just fine. Guessing it wasn't in neutral as you all suggested. Not sure we'll be trusting the Neutral light indicator on the gauge from now on.

drive.google.com/file/d/1ewLAa1jgqzCSRND...Hsr/view?usp=sharing

Still haven't taken it out for a spin yet. Spent some of the day learning how to lube and adjust the clutch and brake cables. Haven't messed with the throttle as of yet. 

We also noticed the fuel line is leaking where it attaches to the carb. We bought a foot of new tubing from a local motorcycle repair shop, but not clue as to what size. It was a bear to get on, I know that. There is no clamp on it...guessing that may be the issue?  To be sure though, what size fuel line and clamp would we need for the carb (Mikuni VM24SH)? 1/4" ID...also seen folks recommend 7mm on the forum.

Thanks MarkT for figuring out how to update the title!

Blimey--well there ya go. What would i know haha. Always something new to catch us out. Great stuff anyway.

I've found 5/16" fuel hose fits well on my carb barb, with a small spin-down hose clamp. 1/4" was too small. BTW today I rode with 20 PSI front and 24 PSI rear, and it definitely corners better on pavement. I'll do 24 and 28 next time, as recommended in the chart Mark posted.

Resolved the leak in the fuel line. Idles much better, though doesn't seem to want to drop below 1600 - 1700 rpm. Afraid to back out the idle mixture screw much more. Is this a good range or should it really be between 1300 and 1400 per the manual?

Also, we attempted multiple times this evening to put in first gear (holding the clutch in) and it lurched forward and died each time. Thoughts on what the issue might be?  A few Google searches indicating an issue with the clutch plates being frozen...perhaps because the bike has sat for 20+ years? The neutral indicator light is no longer coming on when in neutral. Any chance this could be related?

Stuck clutch is common, and it happened to mine as well. Many here suggest zip-tying the clutch lever to the handlebar overnight, and sometimes the plates loosen. Don't do what I did, before asking here... holding the brakes, clutch lever in, revving and punching it into first. I did work, but then slipped badly, so I replaced the friction plates. I could have done other damage as well, but 2K miles later, no issues. Are you sure it's in neutral? Bulb may have blown as well?

You might be in a "false neutral". Rock the bike back a forth a bunch while continuing to downshift a few dozen times. Then do the half-click up to neutral.

You mention 'afraid to back out the mixture screw any further' with a high idle.
I suggest screw the mixture 'in' to 1.25 turns out & back out the speed screw to slow it down, which is different to the mixture screw. Mixture is on a steep angle. Speed screw goes straight in to the slide--under the slide kind of,--without seeing it & guessing a bit.
Be sure you have cable clearance at the carb top when trying to slow the idle down.
Sorry, just wondering if you have the two screws confused, that's all.
Re the stuck clutch. If ya lucky--very lucky after 20 years--you could paddle it along with motor running then drop it into gear & get into second.
After that then go rapidly on & off the throttle & 'might' free up.
Remember to hold the clutch back to the bar while riding.
If it does free it'll be instant so don't get a fright.
So if it does, then give it a good work out & tie the lever back overnight--maybe every night to be doubly sure until you go in there sometime to clean the plates up & steels of rust etc. I had luck doing that with an HT1 90cc that'd been parked for a similar time outside corroded alloy & rust everywhere.

Bungeed the clutch lever all day today.  This evening, we warmed the engine for a bit, shifted to 1st (didn't stall), let off the clutch slightly. and off she went...just down the driveway a bit...but it’s a start.  . Thanks so much for the help. Working on this bike has been a lot of fun.

So...we haven't messed with the transmission oil to this point. Is now a good time to drain and refill?

Regarding the idle, I adjusted the air adjusting screw slightly and that seemed to help a bit. Have it around 1500 rpm right now. Will continue to play with it until we get to between 1300 and 1400. drive.google.com/file/d/1SSNAUoKuAmZrRdz...JPp/view?usp=sharing

Yes change the transmission oil be sure it’s motorcycle oil for wet clutch  10w-30 or10w-40 small screw is the air mixture big screw for idle speed

Change your oil and go for a ride 10 miles or so then check your idle some bikes idle a little higher enjoy your ride and be safe