I have noticed that when I drive at night, apply brakes, sometimes the headlights and dashlights dim for a second.
Any Thoughts

Its a 69.
Do you think I might have a problem somewhere or do they just do that sometimes.
My other old cars never have done that.

Attach a volt meter or a multi-meter and verify how many volts you are getting ... Also, make sure that the belt is sufficiently snug ... Are you running any other accessories such as stereo and big amp ? If so, and you are running a small alternator ... like 37 amp or so, move up to a 63 amp alternator ... OH ... one other thought ... since you say dim for a second, is this when you turn on the signal ? Or, does it happen when you hit a bump or something ... If happening when car hits a bump, you may have a loose wire ...

When I turn on the turn signal, The dash lights dim when it blinks

Measure voltage where?

No accessories.

Measure volts ... a voltmeter can be purchased for $12 or so ... it has a switched hot connection, a ground, and an illumination circuit ... Of course, one with an analog display gives you an approximate reading ... a multimeter or digital meter will give you readings in tenths or hundreds and is more precise ... You may see 13.8 to 15 volts or so ... it is not totally uncommon to see small movement of voltmeter or light flicker as additional load draws power ... the thing you look for is a "big" dip in readout or an indication that your charging system is inadequate ... BTW, with multimeter you can connect to + and - on battery while car is running ... have a friend operate lights and accessories as you monitor readout flucuations ...

Another place to check for Corrosion and possibly loose wiring is the Radiator support Junction Block. I had the Light Flutter problem at Idle and Changed the Voltage Reg, Altenator, Batt Cables, Checkes all Grounds that were accessable and Visual, Tightened the belt almost Guitar string Tight, And still had it before I remembered this Junction Block Being there.

Finally when Cobwebs Cleared Took off the wiring there Cleaned it and the wiring terminals re- assembled it Problem solved.