Hi,
The trick with using LED's as power line power indicators is to use a high brightness LED and keep the current down to an average of around 0.75ma and that keeps the dissipation under 1/4 watt on a 120vac line. For other power line voltages you would just adjust a little.
For a 120vac line using 1/2 wave rectification an 80k Ohm 1/2 watt resistor does not even get warm. The power is roughly 120*120/80000/2=0.09 watts, and this is more than 5 times less than the power rating of the 0.5 watt resistor so it stays cool. This is necessary when the LED and resistor must be mounted inside a closed space where it doesnt get much air flow. If you can mount it where it gets air flow then you can use a lower power rated resistor.
For 350vdc and the same current of 0.00075 amps, we get a total resistance of about 470k. The power dissipation would then be 350*350/470000=0.261 watts. Using two 220k resistors (in series) each 1/2 watt would do it nicely, as that would be enough overrated so the two resistors dont get too warm. The resistors have to be in series so their voltage rating does not come into question (175v each).
One thing to check is to make sure the voltage does not increase too much when the amp is not being used but still turned on.
So the key really is to use a high brightness LED so you dont have to pump too much current through the LED, and that keeps the resistor power dissipation down low enough to be a practical solution. Typical LED brightness ratings are 10000mcd or better. If you try to use a 'normal' LED you might find that it is not bright enough to run on very low current, it should be a high brightness type say around 10000mcd or better.
BTW neon bulbs do run on DC with the proper current limiting resistor. There are at least two sizes though each requiring a different value resistor for full brightness. The thing i dont like about them though is that they do burn out after some time. LED's run at very low current like 1/20 of their normal rating can last literally for 50 years, on for 24 hours a day 7 days a week.