There are umpteen books, tapes, videos, and teachers for folks who want to learn to play acoustic mandolin. I wish I could say the same for the electric. Below are the resources I have been able to track down so far. I haven't personally checked these out, but I hear nothing but rave reviews from those who have.

by Niles Hokkanen & Richard Thompson
2 books (144 pages) / 2 cassettes (2.5 hrs.)

Ahead of its time when it was published in 1983, this method examines the techniques and vocabulary of electric guitar playing and adapts those to the electric (and acoustic) mandolin. Co-written by the Richard Thompson of Fairport Convention fame, one of the most expressive guitarists to ever come out of Great Britain.
     A wide variety of topics are covered and explained in the method, including:
  • Electric string gauges
  • Hammer-Ons, Pull-Offs and Slides
  • Single String Bending
  • Double String Bending
  • Steel Guitar Licks
  • Pinch Harmonics
  • Bending Behind the Nut
  • Blues and Rock 'n Roll Vocabulary
  • Country Chicken Pickin'
  • Rockabilly
  • Playing with the Pick and Finger(s) Telecaster style
  • Electric Celtic Techniques
  • Discographies
and more...
Even if you don't have an electric mandolin, but are an intermediate+ acoustic mandolinist, there's more than enough material which can be played on the acoustic. You may not be able to play all those string-bending licks (using string bends), but you can use hammer-ons and pull-offs instead. Electric guitarists use different phrasing, vocabulary, and techniques than "traditional" mandolin players, but you can incorporate these elements into your mando playing to sound more convincing in genres such as blues, rockabilly, honky-tonk, and rock, as well as spicing up your bluegrass.
     This book is out of print.

by Joe Carr

On this videotape, Carr teaches the "hot jazz" style of mandolin. To help you develop your chops for some great swing and jazz mandolin solos, Joe covers several jazz standards in the style of Johnny Gimble and Tiny Moore. Joe shows licks, scales, and solo development ideas for the standard mandolin and also for the five-string electric mandolin. Available from Elderly Instruments in Michigan.

by Rich DelGrosso

In this monthly column for Blues Revue, Rich covers blues guitar and mandolin techniques as used by such players as Yank Rachell and Johnny Young. He also writes for Mandolin Magazine.

by Tiny Moore 

Forty-eight pages with 14 tunes, as well as licks and exercises. I've heard this is a great book—but, sadly, it's out of print. Good luck finding one.