Odds are you don't need to have the disposal on a GFCI circuit and you probably don't want it there. I understand that a motor can cause GFCIs to trip, you can read up on that somewhere and find out for sure. Or, what the heck, you're an Engineer, we use the scientific method, try it out and see for yourself if it works or trips, it is easy to switch it from on to the other.

The two GFCI circuits you are considering tapping could be your required 2 kitchen small appliance circuits, if that is so you can't put the disposal on either circuit, not allowed by the NEC. In fact the disposal may be required to be on its own 20A circuit, I'm a little hazy about that but I think it is so, your inspector will let you know.

If this is an extra circuit and a dedicated one isn't required then I would tap off the LINE side of the GFCI. You will need 12/2 wire, one black, one white and one bare copper, run that to a switch and then from the switch to the disposal. If you want the disposal to be ground fault protected connect to the LOAD side of the GFCI. When I say side I really mean the top pair of screws or the bottom pair of screws, they will be labeled LOAD and LINE.

You can do this yourself, it is a lot easier than calculus. Just make sure that the current is off, turn off the breakers and use your meter to double check, and don't let anyone turn it back on while you are working on it. The 12/3 circuit might have a double pole breaker but it probably has 2 separate breakers, make sure you turn them both off. And while you are at it make sure the red and black wires are connected to breakers on different busses in the breaker box. The voltage in the busses are 180 degrees out of phase so if on opposite busses the currents cancel in the white wire and it never gets more than 20A, if on the same buss the the currents from the red and black ADD and you can get 40A in the white and a fried wire and maybe a fire.

There are lots of little mistakes that can be made and some can lead to problems, so read a lot, get a book on home wiring, ask questions but don't trust the answers until you check them out. A lot of people sound like they know what they are talking about, they even believe they know but they don't. I might be one of them.

Good luck.

Here is a link that might be useful: wiring kitchens

I don't know about US code, but in Canada a garburator (garbage disposal) must be on its own circuit. A 15A is considered adequate, but a 20A is recommended.

Thanks for your help. There is also a 14 gage wire that goes to the outlets in the rest of the kitchen.
I had two licensed electricians look at it. One was going to splice from the dishwasher and the other was going to splice from the outlet I would be using. I asked both if it was per code and would they guarantee it in the contract. One was so expensive and the other didnÂt show up to do the work, so I told him to forget it. After doing research about it, I decided I might try it myself.