I use an umbrella as my primary rain cover too, and I’m mostly an eastern hiker (AT and various PA area trails.) I started using a small folder (about 6.5oz, 32" dia.) and carrying it. I’ve since finally been converted to a trekking pole user, so now I’m switched to a larger, golf-type umbrella, the lightest I could find with a decent diameter (about 10oz and 42") with the handle cut off (I have a slip-on foam one) and piece of nylon tape sewn into the upper back panel of my pack, just below the lift strap.
I shove the handle-less shaft down into the sleeve and it stays just above my head and slightly tilted back. When not in use I stow it in the left side pocket, shoved down through the compression strap at the top. I find that most of the time this is all I need, and it gives me a canopy to do other things (like dig in my pack) under.
Strategic