It would probably fall under electrical, or electronic engineering, but you could probably do it yourself!
When you say waterproof does the enclosure have resist submersion, or simply a spray of water?. Both are acheivable. Die cast boxes can be made fairly waterproof, simply by using a rubber gasket, between the box, and lid. Likewise you can get IP55 connectors/switches/LED displays etc. if you pour potting compound into the box then all your components will be surounded by "rubber" so there'd be no chance of mosture getting to them. You've got to be a little careful, as potting compound gets fairly warm when curing. Also it insulates heat, but that needn't be much of problem, simply place power-transistors etc so that they are thermal (not electrical) contact with the outside of the box.
I'd go for an electric timer, with a relay/transistor to switch the motor. I'm guessing that you are wanting some way of altering the time delay, and while it's overkill I'd do it use a PIC microprocessor, and use that to control a relay/power transistor.
You've already got power going into the box so you don't need a battery. If the voltage is between 5 and 12V all you need is use some capacitors/diodes to make sure that any voltage surges when switching the motor on/off don't affect the controller. If the voltage is higher you'd probably be looking at a PSU with a transformer, or maybe some kind of switch mode PSU.
Controls could be mounted on the outside of the box, but I think a better solution would be to have the "control" wires exit the box, and be feed to a seperate control box placed in a convient accessable location where they don't need to be waterproofed. The microprocesser makes it far easier to cater for long cable runs. If you really wanted you could implement a proper comunications bus, and create a network of sensors/actuators, that if you wanted could be controlled via computer/telephone/internet etc
So, depending on the voltage, for the switching box all you need is a die-cast box, some potting compound, 1 waterproof connector (large enough to hold your power cables, and control cables) some strip board, a few wires for interconnect, a capacitor, a few diodes, a pic, an IC socket, a power-transistor, and a mica washer (to insulate the transistor from the case, but let the heat though)
The control box probably doesn't need to be waterproof, (but it shouldn't hurt if it is). If the distance between the control/switching box isn't too great, then you may be able to wire the input components directly to the pic. If not you'll need to convert to signals to a format more suitable to travel the required distance (I'd probably use a PIC to do some kind of encoding, and then use a level changer to output the encodered data at higher voltage)
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A 555 timer circuit could easily do the job. Just a little worried about the effects long wires would have on it's function.