Starting truck

Hi, well this morning i bought new starter relay and after 1.5 hrs i was ready to start the truck(yes i replaced relay it fired right up witout any problems, few minutes later i shut it down. About 15 min later i did it again but this time for some reason i was looking at volts it had 12.8 before engine start, but right afer engine started volt began to drop to 11.8 wow i was ####tingg my pants i tried to shut truck but it would kind of make sound like its trying to start up so i turned key to on again and it started. At this point i was just looking when the fire was going to start, well after about 30 sec volts jumped back to about 13.8 and at that point i was able to shut it down. So i took ###### thing off and connected wire to firewall solenoid as swaan said but its no go, same thing is happening???? Whats going on??? Whats could drain batteries for that period of time?

 

Hey me again did some more diging and this morning i installed cut off switch on negative cable and after starting truck if i cut it off with switch and turn the switch back on, volts dont drop?? Now all cables/wires are in the right place, so i know thats not the issue. Could starter solenoid be the problem.

 

This one

 

Yes but if i cut off chassis ground for 1 sec it charges normally.