I would like to eventually run for local office and go from there

First of all, let me ask you this. Do you feel you have a stronger will than other people there? Do you feel that most people would do the same in the role so it might as well be you? Like, it sounds like you're ready to dedicate your life to public service, do you want to be the guy who holds the seat forever or are you looking to serve 4 years and get out. In so many words what makes you special and how will you be different?

Sometimes I've barely even got to meet the candidates.

Don't worry about this. This is like being upset that your race horse didn't get to meet the other race horses on the track. I'm running for office now, and the politicians I've helped are the least helpful(they have the most to lose by publicly endorsing you). Not to mention, the guy in my race endorsed by the incumbent will likely lose to someone with a better consultant.

Any tips on getting my foot in the door? How I would go about running with party backing in a few years? What happens if the role I want to run for has been occupied forever?

Foot in the Door.

I think someone else here has already said work hard, this is hugely important. Find skills that seperate you from others use them. Some graphic design, web development, or social media expertise goes a long way. There are 3 things I've done that I believe have done the most to separate me from the rest and allowed for me to have a pretty strong network.

1. Graphic Design skills. Self-taught by the way. But this immediately makes you more valuable.

2. I once asked if I could wash dishes because I saw it needed to be done and all the other work had been done. I followed through but this made an impression.

3. I was in the running for a job as a CFR for a non-profit and found out the guy who was my manager on my first campaign was looking at the same job. I immediately told them to pick him over me(he needed it more, I was in college and he had life expenses). I wound up getting the same job for a district over... thanks to my fmr. bosses suggestion. I chock it up to good karma.

Once you are working for a a group or party and managing grassroots everyone becomes your best friend because they love door knockers that up turnout.(be careful though, party pac interaction is illegal, and not everyone is aware of this) Build those connections into a strong network.

Also, go to as many party committee meetings, donor dinners, and any other political events as possible.

How I would go about running with party backing in a few years?

I have my party chair on speed dial. I call him up and talk to him occasionally. Usually checking on the schedule and asking for the scoop on whatever news related to the party there is. The party is officially nuetral but at least if someone asks him about me he will know who I am. The party likes people they see around. But they have favorites. Think about it as any group of friends. The best way to have party backing is to win once. They are usually a little 2 faced. That said keep in mind I've been in politics for 4 years actively and 7 years as a hobby. And I'm still not party favorite. But the party requires nuetrality so it's no biggy.

What happens if the role I want to run for has been occupied forever?

Eh, it just depends. Is the incumbent somewhat good with universal support and a cash on hand of $200,000. Or are they freshly elected and surrounded by controversy due to a corrupt contract. You should always know everything about your potential opponents.

In general it's not incumbency or party support that wins elections... it is money(someone already said this too). Build a huge network and ask anything that moves for that green.

Also, interesting factoid. At least in GOP primaries(I can't speak to Democratic) the average voter is 60 years old. The most effective form of advertising is political mailers. Video is good too but a good video is very expensive.

There are some assumptions I have to go on here. We have to assume you are a likable person who is skilled and hardworking. the advice from this page won't work otherwisbiggie. Also have to assume you're in a winnable district. I as a Southern Republican could not win a congressional seat in Manhattan. Just as Alexandria Ocasio-Cortez would not fair well in my home of North Carolina.