It's likely that if the body of a guitar has any effect on the string timbre it's likely so small as to be inaudible given the coloration a signal chain of pickup- electronics-cable-pedals-amp-speaker-room imparts on guitar tone.
The purpose of a solid body electric is to reduce and deaden resonance as much as possible so that maximum volume before feedback can be achieved. Most pickups are wax potted to prevent the internal coils from vibrating and picking up noise microphonically. The pickup does not pickup sound- it merely senses vibrating metal that disturbs it's magnetic field. This is why electric guitars never sound like acoustic guitars- it's sensing an isolating string vibration.
The major factors influencing timbre are the type of pickups (and placement) the nut, the bridge and how or where the string is struck. Whatever the string is directly touching influences how it vibrates. The body is the furthest from the string. Vibrational energy has to pass through the nut and the bridge, then into the neck and the body. The string vibration is already very weak- these vibrations get weaker as they pass through these mediums- where some energy gets reflected and some passes through. Feel the body vibrate with your hands after you strike the string and listen to the string acoustically- hear any difference in timbre? I don't.
I can hear the difference between single coils and humbuckers, can tell if it's a neck, middle or bridge pickup etc, but I've never heard if anyone being able to identify wood species based on amplified tone given the numerous factors in between.
Listen to amplified acoustic guitars. They pretty much all sound electric, negating much of the coloration of the wood box. A pickups job in life is to isolate the string sound from the body of the guitar- if it isn't then you're feeding back uncontrollablly.
The last example is that of Shovelman- he plays a -you guessed it- a shovel, with pickups and a nut and bridge to hold the strings. No body wood to speak of- it sounds pretty much exactly like an electric guitar.
The only thing your body wood is for is to be a frame for everything to stay held together and maybe to look pretty. It could have an influence on sustain if you have a good contact between the string bridge and wood, but not timbre. You'll control timbre through your amp, pickups and how you strike the string.