I considered and rejected many ideas, but finally settled upon turning a big 20-inch plywood wheel with an electric motor and getting my reciprocation (up/down elevator action) from an off-center bolt fastened to the wheel. No motor I found turned out to have both the right speed and the right power, so I ended up installing a chain-and-sprocket-based speed reduction system.
The end result was an elevator that took 7 seconds to go either up or down. I installed position indicator contacts made from unused prong fasteners (for binding punched paper reports—ask any stationery store if this is unfamiliar—see figs. 6 and 7) to light up 12-volt indicator bulbs (hooked up to my layout's 12-volt lighting bus) to let me know when to shut down the motor when the elevator was either all the way up or down. A screw sticking out of the rim of the wheel operates the indicator contacts.
This would have been a nasty timing issue for the elevator operator (who do you know that can time toggle operations to within a split second by hand?) except that when the wheel is in operation, it doesn't actually move the elevator much when the off-center bolt is between 5 and 7 o'clock or 11 and 1 o'clock, so making the elevator stop at the right place required no more than a normal reaction time response from the operator. When I start up the motor, I wait a little less than seven seconds and a position indicator light goes on, so I shut off the switch. The indicators need to light up when the bolt position is at 11:40 and 5:40—this suffices to get the bolt stopped at the needed 12:00 and 6:00 positions. If you want a slow reaction time to suffice, install the contacts so that 11:30 and 5:30 indicator lights occur—or even "earlier."
Pulleys and thick string transfer the reciprocating action from the bolt on the wheel to the 15.75-inch-long logging elevator, which is hoisted 15.5 inches, or over two inches per second. (See fig. 2.) The motor is an Oriental Motor Co., Ltd. Product (115-volt, 1 amp—less power doesn't work: I tried it) I got from a surplus electronics store with 2900 rpm (48.3 rps [revolutions per second]) and a 1:11 gear reduction box connected to it (which gave 4.4 rps), but it was four times too fast (I needed about 1 rps) so I hitched it up to a 10-tooth to 40-tooth chain and sprocket speed reduction system I built from parts from the local sprocket supply house. The roller that turns the big wheel is a simple 1-inch sanding cylinder roller available at any hardware store.
Because the elevator is centered in some benchwork on the Squirrel Valley Railroad, it had to be built first, and the 4' x 8' benchwork lifted over it, in order to preclude future logistics nightmares come installation time—it's 6' tall!