Could very well be the alternator. That said, I wouldn't rule out a connection, at this point. Just to eliminate possibly having to dig out the alternator, I'd wanna see what the voltage was at the battery with the turn signal on, and then the lights. Normally, it should be around 14.7 VDC (cold). If the alternator/regulator is going south, voltage will be "something" other than a steady 14.7ish with the lights and or the turn signal on.
How-some-ever, if there is a ground or B+ connector issue in the wire harness between the battery and the various ciricuits, the voltage at the battery will remain more or less constant while the voltage (on the other side of the fault) will drop significantly.
It may well be the alternator/regulator, but I'd wanna see voltage fluctuate at the battery before I pulled the alt.
Just my 2¢ - and prolly not worth that!
P.