I think you have to be a damn fine drummer first and foremost. People have to want you. You will be sought out if your playing strikes a chord with other musicians. You have to be the guy/gal that the good musicians want backing them up. They want someone who can play anything that comes their way, confidently, and someone who has a good working knowledge of many songs and styles. A drummer who truly understands exactly what role their instrument plays in an ensemble situation, and someone who actually executes this understanding in a fine fashion is the first criteria to be met. Having a solid sense of time and tempo cannot be understated. I hear a lot of drummers whose meter is noticeably unsteady, or who aren't feeling where a song wants to be tempo wise. That's Job#1, Time and tempo. Making a song feel good is a skill that's hard to quantify exactly what that entails. How do you learn how to feel things deeper? And if you do feel things deep, you have to have the skills to be able to communicate that deep feeling through your drums.
There are so many different aspects that have to be met...A great drummer has to have a lot of understanding of what the music requires. The nuts and bolts aspect. Good tempo, steady meter, knowing what not to play, (epic important) knowing what to play, playing it with the proper energy, not too much, not too little, having control and an understanding of your dynamics...a critically important thing you can do as a drummer is to understand exactly what each player needs from you. Like a singer needs your support, but you have to stay out of the way. A guitarist needs a solid backbeat to craft his solo over and not a lot of fills, it's their time. A piano player needs you to watch your volume and be thoughtful because you can overpower them, for their solo. And with every solo, you have to rise and fall with the soloist...basically listen to them and react with your drum part to custom fit to their lead that night.
After that, being nice and reliable will keep your gigs, but people have to want to play with you first. And people for sure will make it a point to seek out an awesome drummer, because they are rare. We are the most "make or break the band" player up there. IMO.
I think it's hard to be a butthole if you can support the other musicians well. If you can get past yourself and listen to the others, and play off them or with them, instead if in spite of them, then to me that means you have empathy for others and can hear where they are going. You have to read their minds, that's what I'm saying. If you can do that, that's a high skill. It's hard to be a butthead when you have empathy for others.
I'm a musician who plays the drums. I have to say, most drummers I see don't think like musicians, not even close. They may have the physical skills necessary, but they lack a real understanding of exactly what needs to be accomplished up there. They are just looking for a spot to squeeze a fill in. A lot of guys think the drums are the center of attention. They have so far to go mentally, no wonder no one is requesting their services. Just because I can cast a fishing rod, that doesn't make me a great fisherman. Same with drumming.
If you play great drums, and are out there, you will be sought out.