I'm having brake light problems on my 1996 k 1500 pickup. My all my bulbs are working , but when I turn on running lights it causes my brake lights to go out and makes my signal lights to flash faste

To get a wiring diagram for your 1995 Dodge Ram 1500, you can visit a website such as AutoZone.com. Once you have the diagram, you can use it to help diagnose the issue with your brake and running lights. It sounds like the issue could be caused by a faulty ground wire or a bad connection. If the ground wire is disconnected or corroded, the lights will not work properly. Additionally, the problem could be caused by a bad connection between the bulb and the socket, or a faulty bulb. To test for a bad connection, use a multimeter to check the voltage at the socket. If the voltage is low, the connection should be resoldered or replaced.

Common Problems with Chevy & GMC Pickup Trucks ' 1988-2013
https://raybuck.com/common-issues-with-full-sized-gm-pickup-trucks/2022 RAM 1500
https://cdn.dealereprocess.org/cdn/servicemanuals/ram/2022-1500.pdfIntermittent Failure to Start : Chevrolet Silverado 1500 Electrical and ...
https://repairpal.com/intermittant-failure-to-start-743

bad or disconnected brake light switch

The brake light bulbs could be at fault....They are designed to work with the brake pedal and the night running lights....The bulbs work as a two way light....This means they have 2 small wires inside the bulb...Some bulbs only have one wire but they only serve one purpose...In cases like that the bulbs are at fault normally or you have a bad wiring issue ...,there is also a brake light switch connected to the brake pedal but if your brake lights work it should be ok..but don't rule it out...anything is possible with older vehicles...Only one wire inside the bulb can burn out and cause one light not to work but the other light will work because the bulb still has one of the wires connected inside...One 1157 bulb works 2 lights,,,the brake light and the running light....It is common for them to blow only half way leaving the other light working ....Look at the difference between a 1156 bulb and a 1157 bulb and you will see what I am trying to describe..An 1156 is for only a one way light because it only has one wire....look at the difference between the two.....If you have never replaced them change them anyway...Sometimes you can't tell when they are blown....Normally the bulbs cause the problem you are having....Thanks

the circuit is shorted to the bulbs somewhere in the wires there is a short causing power to bypass the fuse and constantly run to the bulbs

If you replaced a brake light bulb it may be the wrong bulb causing a back feed from the brake lights to the running lights

check voltage to the sockets, if good check the grounds, if no voltage go to the switches and trace from there

Check the lamp sockets themselves. Pull a bulb and see if the connections in the sockets are bad.

Obviously you have a short somehow power is bleading over to this circuit. You may be forced to do some hard debuging (i.e wiring diagram, test light isolate the problem on the circuit).

If I were taking a guess I would try the following:
1) Remove the fuse for the taillight
2) If the light goes out I would start looking at the dashboard light switch
3) If the light does not go out then I would start looking toward the rear end of the truck wires that are scouffed, trailer light connections ect.

Hope this gives you a start, needless to say a short can take forever to find.

There will be an electronic flasher module located under your dash near the steering column (don't know it's exactly location as it varies). It sounds like this unit may be faulty.

check all fuse for the taillights again, make sure all bulbs are good. it blink fast because a bulb is out.