[...] getting two light gates (one at the top of the ramp and the other at the bottom) and hook it up to the trigger on a standard stop watch. When the first gate is breached the timer starts and the second stops it.
This is just a rough idea, does any one see any problems or an easier way?
The easiest way I can think of (and have actually done a number of times) is to use a cheap LASER pointer and two small pieces of eg. 1mm polycarbonate (or similar clear plastic that's somewhat scratch resistant) for beam splitters for the light to breach and two photo transistors, two regular BjT's, a few resistors and caps to interface the stop watch. You may even get away with using LDRs instead of photo transistors, if you can find two that exhibits identical delays (it's OK that they're slow here, as long as they are equally
slow, as that will give the same net result as with photo transistors).
The timing is be started on the Start/Stop button, but for the "stop", either the same button can be used or the "Lap time" button.
Dissecting a stop watch from a dime store, you'll usually find very primitive contacts, with the button pressing a bit of nickel flashed steel towards another similar bit. With care, it's fairly easy so solder wires to the contacts. If you wire up all 3 buttons (usually Start/Stop, Lap and Mode), you can mount the watch in a box with switches to make it easy to zero the count etc. and if triggered by a transistor (that's itself driven through a cap with a pull up resistor on the basis), manual buttons won't damage the electronic interface.
If/when you get your paws on the watch, do take some sharp photos of it, both initially and when opened - with focus on the contacts - and post the best, if you need help identifying where to solder or something similar.
I have modded a number of very cheap stop watches for similar purposes and as long as you can solder wires to the contacts without burning the plastic they're seated in (a pair of pliers can help keeping the temperature of the metal down so it doesn't melt its seating), the rest is easy.