My mechanic put in a button starter which works pretty good. It is “touchy” and I need to hit the gas just right to get it to catch. Once it starts it runs beautifully but the battery seems to drain instead of charge while driving. When I turn the car off,and then try to start it again, the battery sounds really low, and often dies before I can get it to turn over again. It fires right up with the first sign of a jump. The mechanic has looked for an ignition (says he cant find the right one). Other people have suggested an altenator or voltage regualator…or a short somewhere. I am looking to sell this car (it was my high school graduation present) but I would like it to be dependable to start…for not much money. What should I look for in a mechanic that would be best for this kind of job???
A complete electrical diagnosis should be done and this is not difficult to do.
The battery should be fully charged and load tested.
The charging system should be tested.
The starter motor should be tested for current draw.
The car electrical system should be tested for a parasitic draw. Determining if a draw exists is easy; finding it is a bit more difficult. However, the elec. system on these cars is comparatively simple and it should not be a major job at all IF this problem exists.
Sluggish starter motor operation could be caused by a run down battery or a dragging starter motor.
Any shop that specializes in electrical should be able to sort this out PDQ.
Question. Why did your mechanic install a button starter? Why not just fix the problem correctly? I’m assuming this was done due to the starter solenoid not engaging.
(I’m a big Mopar fan so cool car you have there.) 
Your alternator and/or voltage regulator is not working correctly. A few minutes with a voltmeter should be able to narrow down the problem. If you don’t know how to diagnose and fix this yourself, be prepared to spend some money with your mechanic. The electricals on this car are like 45 years old, and reliability and dependability are out the window. Be prepared to spend more than a few dollars if that is your goal.
What to look for in a mechanic? Someone who understands and can recognize a carburetor is a good first step. Setting up points properly is a lost art. And if this car still has a generator, not an alternator, you’ve lost anyone younger than 60.
In '67, Chrysler still used an external solid state regulator and an alternator. Sounds like one or the other is bad…Simple to check…The regulator looks like a black pack of cigarettes with a 3-wire connector plugged into it, mounted on the firewall…
What engine is installed in this car…?
And make sure the cables and connections are good, and that the belt is tightened correctly.
I’m fairly certain Chrysler didn’t introduce solid state voltage regulators until the early 70s. Your voltage regulator is the older style mechanical version with a bimetallic strip in it. If your normal charging voltage is off, those can be adjusted, with needle nose pliers and a volt meter - though carefully.
The alternator is driven of a “V” belt and if it is a bit loose the alternator pulley will slip on the belt and you won’t get a good charge. Your symptoms are pretty classic for a slipping alternator belt and/or a weak (ready for replacement) battery. If the car sits a lot it simply could need a full charge on the current battery. Should not be hard to sort this out and fix.
Why was there a need for a “button” to activate the starter? Perhaps you have a bad ignition switch?
You might look around for a mechanic who appreciates the old iron and enjoys working on it. Diagnosing such a problem should not be very difficult for anyone familiar with the system. And the push button starter switch might be the result of not recognizing a failing neutral safety switch.
Connect a voltmeter across the battery with the engine off. Read the meter. It should read 12.2-12.6 volts…Start the engine and bring to a fast idle. Read the meter. It should now read 13.5-14.0 volts and be slowly climbing…If it still reads just 12.2-12.5 volts, your charging system is not working…