13V at idle seems a bit low - should be 13.4 minimum from the bosch alternators I have worked on. The higher rev voltage is acceptable but a little low. Some of my alternators went that low but most at higher rev produce 14.0 - 14.7 volts, at idle they never went below 13.4v. If you haven't done it yet - spring for a new regulator/brush pak for your alternator - simple to change and not all that expensive - with 13v idle charge - it is getting ready to let go. Like MB Doc says - not enough power getting through. While you are at it - let the car sit overnight and without starting it - check the static voltage on the battery - it should be 12.4 volts MINIMUM - anything lower (because of your 13V idle charging should bring it up to that) - indicates a bad battery that should be changed. If the battery has an internal short it will suck your charging voltage down and could damage your alternator.
1) check battery first to make sure it is good
2) then check alternator reg/brushes.
I am confidant - that the above should cure your problem