Honestly, if the antenna is literally a random hunk of copper, so is the counterpoise. Make it anything from 0 to x units long and start experimenting. Getting this to work on such a broad range of bands will be a challenge, to say the least.
However, if we consider what you are building not a "random end-fed" antenna, but rather an offset-fed dipole, then there are many references in the usual places for feedline location which then defines what your "counterpoise" is. Though, of course, it isn't called a counterpoise now -- it's just the short leg of the dipole.
But in many ways that is all a counterpoise is: something for the rest of the antenna to work against, because if we don't, that antenna will find a counterpoise whether we like it or not. And it'll probably be the feedline, or a human body if that is near enough.
A multi-band single-wire antenna depends on how whole number ratio wavelengths distribute the current and voltage across the entire antenna, the compromises being the resulting radiation pattern and feedpoint impedance.