The most common timers just turn the power to an outlet on and off at specified times. To get more than one "on" and one "off" in a day is likely going to be harder to find. I think there are some programmable digital ones out there that will do that, but they will be significantly more expensive than a basic timer. The cheapest of timers have a rotating dial that is kind of like a 24 hour clock with pegs that slide into place for on and off. I suppose if you really needed the kind of control you're talking about you could buy a couple of the same type to steal the pegs from one to add onto the one you'll be using.
I'm not familiar with the solarmax fixture. If it was just plugged into the wall (no timer), can you turn each bulb on and off independently? If not, the timer can't do it for you either. If you can, does the fixture operate off of only one cord, or does it have two? If it only has one cord, then the timer can't control both lamps independently.
You also asked about if the fixture required a switch to turn the lights on and off, would a timer work? I assume you mean a switch on the fixture. If I understand you correctly, then you would just leave the fixture switch on, plug the fixture into the timer, set the timer as desired, and plug the timer into the wall. If you meant that the outlet was controlled by a wall switch, the you'd have to leave the wall switch in the on position.
It is a violation of federal law to use this product in a manner inconsistent with its labelling.