You realize that as a General Class operator, you will be able to administer Technician examinations only. You will not be able to handle any exams for General or Extra class. My suggestion is to upgrade your license to Extra as soon as possible. This makes you more valuable to the VE team.
Talk to your club's Contact VE (the person who is in charge of their testing) and they can help you through the process. It's pretty simple, but if not done correctly can cause the application to be rejected. While it's true that you can get certified through the ARRL, this will make it difficult for you to assist in your club's testing sessions (since they use the W5YI system and your certification is through the ARRL) so it's best to keep it simple. You'll need the Contact VE to sign your application and accept you as part of their team anyway so starting there is best anyway. While you will be limited by your license class to what tests you can assist on, that's generally not an issue unless the testing team is only the minimum required. Most testing sessions are for new hams testing for their Tech license so you will still be of good use to your team. Now if others are upgrading where your license class prevents you from certifying those upgrades, other VEs can work on those upgrades while you handle the lower class certifications.
On another note of the same topic, anyone know on average if there tends to be an oversupply or shortage of VEs though it's locale specific (if you're a local testing contact, do you tend to have trouble arbitrarily finding two others at minimum to hold an examination)? Just wondering how hard it is to keep up with the requirements to administer exams to keep certification (I suspect rotation is used if there's a lot of VEs, but can it ever be too many VEs for a locale, or is it frequently tough to find people?)
I looked into this once. You have to be an Extra. If they schedule a testing session they have to be able to test for all license classes.
If a test taker passes the Technician they let them take the General, and if they pass that they can take the Extra. If their VEs were not Extras they could not do this. You may be able to help out with a Technician class but they usually still need three Extras there.
I don't think it's illegal to simply say they can't handle testing General/Extra if they could get only two Extra VEs and one General VE, yes it would be annoying for upgrades but hey, they're volunteers and can say no.
However, it seems at least sometimes their sessions have more than three people there, at least there were more than three VEs there when I got my license. Three of them must have been Extras however (I don't recall if there were more than three Extras however, I don't remember their callsigns but I do recall there being at least two 1x2 or 2x1's, and one A-series 2x2), but there were at least 15 or more people taking exams, most of them were getting Technician, so the added bandwidth would help out the Extras. Yes unfortunately the people who passed Technician and tried for General would have to go through the Extra VEs, but surprisingly there were a few people who didn't want to try General (and one that tried it and said they were "owned" by the General exam...)
Incidentally the local VE contact was not there when I took my exam, so likely there was some rotation going on there.
I suspect the fee divvy-up is the last aspect of the proctoring for ARRL-VE (or W5YI-VE) I guess something wants to limit the number of proctors. Different story for Laurel-VE I suspect, but I have no idea what happens behind the scenes.
I'm a Supervising VE and I run an average of 30 or more sessions per year. That's broken down into two regularly scheduled Saturday sessions and one class a month. I have an average of 8-10 VEs present at the Saturday sessions and usually more for the classes. (One of our other supervising VEs once had 31 VEs at a class examination session.) Although they're rare, I have worked with General class VEs. There are jobs they can do at a session that won't put them in conflict with the rules.
Years ago, my friend ran a W5YI testing group. He wanted to have a spare tester in case one could not show up. All his testers were extra class with 20 WPM. I too was a coded extra, so I said "why not". It was once a month. He handled all the paperwork, so I signed what he gave me, and was approved a few weeks later. It was an hour once a month, & I was glad to give back.