my old title: "Utility Infielder"
Answer first, questions later.
Pitch yourself as having specific skills. Choose a few of your skills, pitch them. Like, you do your homework about a job, you find out it's a c# networking job, and you pitch yourself as a c# and networking guy. You get the job, you spend 6 months doing the specific job (which will further hone your skills), then you pitch some other job within the group.
This is an essential problem in marketing. I have it in my company (a very fast NoSQL database called Aerospike). Our marketing deparment wants to talk about the speed of the database, because it's fast. And they want to talk about the reliability, because it's NoSQL that does ACID. And they want to talk about our Flash and SSD optimizations, because those are great for lowering in memory database cost. And they want to talk about our happy customers. And the real-time analytics that beat Hana. Or they talk about replacing redis and memcache and hbase. Or our incredibly robust clustering algorithm.
What happens? We end up with rambling statements without a point, confusing everyone, because they throw in the kitchen sink of buzzwords.
Get specific in each resume, cast yourself as something they understand, and once you're in, they'll use you for more and more.
( One word though: you really do have to be an excellent generalist. I run into a lot of people who say they're generalists but know so little about any given thing that they're useless for everything. They hide behind the "generalist" label because they can't be bothered to learn any single thing. If that's you, nut up, pick one thing, and spend two months without a job learning the living daylights out of that thing, then present yourself as an expert, and win jobs at that. You think you're a problem solver? Solve the problem of getting a job as a...I dunno... high scale Python expert, android hacker, whatever you fancy. That's actually another key to the tech industry that people seem to forget, and gets lost in the comments of ageism. Most older techies start to feel entitled and don't learn new things. I was taught you need to spend 20% of your time always learning new languages & skills, otherwise you get stale. Thus I am an over employed late-forties techie.)