Trail running (hills) is the absolute best training for mountaineering and scrambling, in my opinion. I'm talking about long, relatively slow, runs up steep trails and jeep roads. I started running anything that I could- steep jeep roads, steep trails, ridge running etc. I'm lucky enough to live in an area with hundreds of steep forest roads going up to 5000-7000 ft. It's perfect training. When I get in situations where I just have to hike, scramble, or mountaineer, it feels relatively easy after mountain running. Often on scrambles that require long approaches, I just run the approach and then the scramble / climb actually seems easy. This also has allowed me to do 2-3 day climbs in a day, and see some backcountry that most often requires overnighters.
I was never able to do this in my 20's, only since my mid 30's. I attribute that to training smarter now (cross training, nutrition, a rest day every 2 weeks). This type of training definitely takes a little getting used to, but it will give most people the biggest "pop" in their mountain endurance.