First check if the vacuum advance is working:
Unclip the distibutor cap, and move it to the side.
Look inside and you'll see the vacuum advance arm connected to the advance plate.
Connect a hose directly to the vacuum advance line. Suck on the hose and you should see the vacuum advance arm move the plate. It should stay there as long as you keep suction on the hose.
If it doesn't do the above, then you need to replace the vacuum advance.
While you have the distributor cap off, turn the rotor to the right and let go. It should move freely, and then snap back when you let it go. If it doesn't, then you can spray some WD-40 under the plate to help loosen things. Don't use carb cleaner.
You should also remove the rotor and lube the felt under the rotor with about 5 drops of 10W oil (Three in One oil is fine). That helps to keep the advance plate lubed.
There is also a small oil cap at the driver side of the distributor. It's not easy to see, but it's there. That needs to get about 6 to 8 drops of the same oil. It's important, since that lubes the distributor bushings.
You can check the timing doing it the way you do it on your other car. Advance in small amounts and listen for Ping. If it Pings, then back off until it quits.
Auto Zone will loan you a Timing Light -- you really should have one. Good idea for a B'Day present.
1960 Hard Top/430
Thunderbird Registry Number 1231