Repeat timers -- especially short-cycle ones for hydroponic applications are rather expensive. The Weteck timer is $7-8 bucks and can be modified to run in an approximate 44 minute cycle.
There is an on-line YouTube hack for the Westek timer, but when I got mine opened it wasn't the same as the one the guy was hacking, so initially a little panic set is as I had already bought 2 of them!
After I settled down a little and looking at it a bit to figure out what he was actually doing, and thinking a bit, I realized that the one I had could be modified, and it was actually a bit easier IMO to do then the You Tube version.
First the concept is this: The little motor that runs the thing is spinning relatively fast, so in order to spin the output shaft at one revolution per day, the input has to be geared down. In this case there are 6 gear reductions. What we want to do is remove some of the reductions so that the output shaft doesn't get slowed down quite so much.
The timer
you will for SURE need a tri-wing screwdriver (like we needed yet another screwdriver type?)!
remove the 3 tri-wing screws. The dial-side will slide off the top.
Behold the inside!
There are two tabs that you need to get under with a small screwdriver on either side of the mechanism
 
with the top off we can see all of the gears.
Remove the gear on the left. The gear has a ratcheting center that allows the timer to be stepped forward (but not backward).
 
Now the center gear is removed and you can chuck that one -- we won't be needing it anymore. We will be deleting this gear drop and the one it was connected to in order to speed up the output (ratchet gear) .
now remove the exposed gear on the right. This is the one we will be modifying. Take a sharp pin and scratch the upper surface of the gear so that when we glue it the glue will have something to adhere to.
you will need some fiber washers. No 6 or number 8 works OK. The center hole need to be big enough for the washer to slide over the small center gear in the middle of the bigger gear, and not too big to interfere with the larger gear teeth. Scratch the washer surface(s) with a sharp pin so that the glue gets a bite. What we are going to do is glue (3) 0.032 washers to the top of the gear under the ratcheting gear. It is not critical that they be perfectly lines up, but avoid getting glue on the shaft or into the gears. Repeat until all three gears are glued onto the gear.
The washers are slightly taller than the top of the little gear, so the top washer need to be sanded just a bit.
remove the ratcheting center from the first gear removed, and score the bottom with the pin. reassemble the racheting center part back into the gears. Place the gear with the washers on it back in the gear box, apply the glue and put the ratcheting gear back on the shaft (the shaft will line the gears up. Note that there is enough glue between the washer and the gear since you can see the washer showing through (make sure it doesn't get glued to the shaft).
  
line up the motor and then reinstall the top of the gear case
reinstall in into the housing
 And finally, snap the top back on
There are 48 divisions and each division is around 50-55 seconds (it is only relatively accurate!). Anyway, it is close enough for the application (fit for purpose as our cousins across the pond would say!). I'm currently running my cloning machine 00:1:50 on and 00:12:50 off (3 cycles per full revolution).
I hope this is helpful -- it doesn't take long to do and the price is right!!
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