The main reason a gas WH isn't as efficient as electric is two-fold - it has an uninsulated flue going up the middle and not all of the energy gets into the water you're trying to heat - some goes out the flue. But, in most places in the US, NG is MUCH less expensive per BTU than getting the equivalent in kWHrs.
There are potential health risks if you let the water in the tank cool off too much...the stuff can start to grow things when the temperature drops. Keeping it above the typical minimum, keeps that stash of water safe for when you turn the thing back on. Keeping it above 140 may end up being safer, but the higher the storage temp, the bigger the standby losses, and if it had been off for awhile, I'd want to get it at or above 140 for awhile before I used it. All residential tanks should be regulated to no more than 120, and that's done with a tempering valve - required where I live, regardless of whatever temp you choose to set the WH.
I haven't looked at timers for a long time, but the ones I saw when I was uses a motor clamped onto the gas valve to turn it back and forth. The gas valve really wasn't designed to be moved back and forth on a regular basis. As electronics have been applied to some of them, there may be other ways, and some may be offered by the manufacturer as an option.