Looking for some advice. 1) Can I use a mono-cable splitter (e.g. from radio shack) to trigger two different power amps? 2) Are there any advantages or disadvantages versus leaving the amps on all of the time? 3) Any other thoughts?

Background:I have a Outlaw 1050 which comes with a trigger cable. For power amps I have a Parasound HCA-1200IIA which comes with a 12v trigger (bare wire) but I have never used it leaving the amp pretty much powered up continuously. I am getting a Outlaw 750 via ebay (a previous purchase of a Parasound 855 fell through), which also has a trigger.
It seems I could use the splitter to trigger both amps with the appropriate attachments after the splitter.

The Outlaw trigger outputs are typically spec'd at 12 volts, 50 mA (I couldn't find the 1050 manual on line but the 1070 and 970 agree on the 50 mA). The trigger input on the Outlaw amps are spec'd at 5 mA minimum drive current. I couldn't find anything on the Parasound requirement. But unless it's really power hungry you should have no problem triggering two amps off the 1050. I would think you could split it at least 5 times and not bog down the 1050 drivers.

I don't know that leaving today's solid state electronics on versus power cycling them makes much difference. I'd give a different answer if it was a tube amp.

wont leaving them on shorten the life of the amp a little? (not to mention be a total waist of power)

It will consume some power. Whether it shortens the life or not is hard to say - powering on is typically a high-stress event for a piece of electronics and can do more to shorten life than sitting on but idle.

My original thought was like Gonks, I figured as long as the device was on, but not receiving a signal, the power consumption was just enough to keep the capacitors charged, but not really anything else as no amplification was occurring. Don't know how true this was and is why I was asking about the trigger when I get the 750.

That's a tough question to answer because it depends on both the product design and the environment it's operating in. Here's my general list of electronic killers.

1. Operation in high temp / high humidity environments. Moderate heat isn't really a concern. Once the humidity gets above 90% I start to worry about my electronics. The hotter it gets, the more I worry. Under extreme conditions the electronics can suffer from a problem called solder migration which causes shorts.

2. Voltage and current transients. These happen anywhere you have inductive and capacitive elements and you make or break power. You'll get these when you turn on your amp AND when you turn it off. These can cause elctrical overstress which causes components to fail.

3. Thermal Shock. Rapid changes from cold to hot or hot to cold can crack solder joints or cause smaller components to crack (surface mount caps have always given me fits).

Leaving your equipment on you run into the life shortening effects of heat and humidity (#1). Power cycling you run into into the life shortening effects of #2 and #3. Good design can mitigate some of these effects but I can't in general say which would be better. Whoever did the validation testing on the electronics can give you a better idea of where the weaknesses are but they tend to be pretty tight lipped individuals.

Unlike me who uses many words to say I don't know

Thanks for the additional feedback. In Southern California, if you are near beach (like I am), the temperature is seldom really hot and the periods of high humidity don't align with the periods of high heat. Nor is smog a major issue. The only environmental problem, I am aware of is salty air, especially in the winter and June.

Don't know what others' experiences are like, but I have only had two power amps in over 40 years. A Quatre that failed with a cracked board after over 20 years of use and its replacement the Parasound HCA-1200IIA. Perhaps I am being naive but I was rather expecting both the Parasound and the 750 to last for at least 10 more years.

Good power amps can and will operate well for many, many years. Both the Parasound and the 750 should have a lot of life left in them.