How to check brake system failure

On a vehicle of this age you won't get a pedal that is as solid as a newer vehicle. Unless you replace EVERY part in the system you will always get a small amount of 'soft' in the pedal travel.
There are two common reasons for a soft pedal.
-The Callipers have been bled in the wrong order so there is air trapped in the system. The order is commonly - Rear passenger side, Rear driver's side, Front passenger's side and Front Driver's side last. When bleeding brakes take your time to make sure all the trapped air is removed.
-There is a leak somewhere in the system letting air back into the brake lines. Even a pin hole can cause issues.
As there are brake lines running underneath the vehicle they can get damaged by loose objects on the road and as this is a 1968 car it could be worth you replacing all the brake lines for new. Some older car manufacturers used steel for the lines so they rust out. There are companies out there that supply Stainless steel systems that won't rust.
Try this method for bleeding the brakes. I'm assuming your vehicle is fitted with a brake booster.
Start with the calliper or drum furthest away from the brake reservoir and use fresh brake fluid of the correct DOT number. Keep checking and topping up the reservoir while you are working to avoid running the system dry. Once all 4 wheels are done pump the pedal until it goes as hard as it can. Press and hold the pedal down and start the engine. Let it idle for about a minute. As it starts you should feel the pedal soften. This is the engine creating the vacuum pressure the booster works on. Pump up the pedal again it should go hard. Turn the engine off.

Bleed all wheels .farthest one first .

it is air in the lines
Take it to an accredited brake specialist shop and have the brakes bled

Why did you change the brake pads? Was it because there was already a problem with the brakes? Or just because they were worn out?

It's quite common for the failure of the brake master cylinder during/after bleeding brakes, especially if it's the first time for a long time that they've been bled. The reason is simple: during operation, vehicle braking systems take water from the atmosphere into the brake fluid. This does a couple of things - reduces the boiling point of the fluid; and begins the inexorable process of the corrosion of the inisde of the brake system components. This also happens within the brake master cylinder, and creates a 'use ridge' at the place where the piston stops in normal operation. When you bleed the brakes, you force the master cylinder piston beyond (across) that ridge, and sadly this often tears the fine sealing edge off the master cylinder piston seal, leading to a soft pedal (at best) or one that goes through to the floor (at worst). Obviously I can't tell you what's happened to yours, but it will need someone to check it out properly or you run the risk of having permanently unserviceable (and potentially unsafe) brakes. Good luck!

If you replaced the calipers and the brake pedal is still soft the most common issue is air in the system. Check master cylinder and fill if needed, make sure all lines to calipers are tight and no apparent leaks, have a helper pump the brake a few times and press down holding in the down position (to the floor). At that time loosen the bleeder screw on the caliper releasing the fluid and air in the lines. A rag is recommended to cover floor. Do this on all calipers that were replaced a few times one at a time untill all air bubbles are not present, a clean flow of fluid . Make sure to have x-tra brake fluid on hand and check the master cylinder periodically (fill if low) and proceed with the bleeding process. If you allow the master cylinder to go dry and **** air the process of bleeding the brakes will have to be started all over again, so keep master cylinder level full after a few cracks of the bleeder. best of sucess to you !

There are sensors on each wheel. The sensors will have wires connected to them and they will stick through the backing plates or calipers. Next are the round metal plates which turn with the tires.

These 2 parts can get magnetized brake dust and steel dust on them and they will misread the revolutions of the tire. You want to clean them as best you can. Also check the Emergency brake system inside the rear rotors. Check the drum surface inside the rear rotors as most tend to corrode and the metal flakes off. The flakes can cause the ABS to misread the revolutions.

If all is well and clean for the sensors, they only 2 things left are the Proportunate Valve and the Master Cylinder. With a light touch, the Proportunate valve may slow one end of the car first, causing the ABS to activate. If the Master cylinder is not shooting the correct pressure to all discharge ports with a light touch, there can be a difference in volume sent to the Proportunate Valve triggering the ABS.

The pressure can be measured, but the cost of doing it may exceed the cost of the replacement parts. You may want to go to a Salvage yard and find a car with a sealed system and get your parts.

Air can be a pain to get out sometimes. Check for striped fitting/bleed screws, if it all check out, it is most likely the master cylinder on the firewall.

is it the "red" brake warning light? if so, its possible the master cylinder may have an internal leak causing the pedal to be soft. if this is correct you'll need to replace the master cylinder.
If this is the "yellow" brake warning light it the ABS system (anti-lock brake system) you'll need to have a professional inspect this.

You brake master cylinder is either low or faulty. Check your fluid level, if that is good you need to have this repaired as soon as possible as it could lead to brake failure.

bleed the system