EBG does not refer to electric bass guitar, but the Yorkshire exclamation aimed at a new-fangled, musical doohickey "Eee, by gum"
Fender did consider making a guitar for the Yorkshire market, the Tadcaster, which was much like a Broadcaster, but not so fancy. The matching bass was to be the Lancaster, a P bass with only the bass side of the pickup as there's no point in wasting money on a whole pickup when you'll probably never use the other two strings.
Fender showed that he failed to understand the Wars of the Roses with this choice of names as no Yorkshire band would have a Lancastrian instrument in it, and vice versa, and no London band would have either.