If your sausage is in a natural casing and it puckers, that is over cooked to me, and it seems like 90 of places cook it that way!
Brats, I was taught by Phrett & Jeri that you boil in beer, butter & onion solution and finish on hot grill, excellent technique. Your German Texas beef sausage, I guess I am not real familiar with it, if it is like a brat, I highly encourage you to use that technique. A good old hot dog, I am a boil or steam guy, but grill is not far behind. Not sure if either of the next two are like the sausage you are referring to? I made a TX Hill Country Sausage once, it adapted well to being quick grilled. I have heard of a Texas Hot Gut sausage, not sure if I have ever had it, but I think I did when we were in Lockhart, TX at the Chisolm Trail BBQ. To me, it lent itself to a Smoke Temperature, about 200° till cooked and the insides mostly firm. But it also seemed to be a sausage that the casing was not eaten, almost squeezed out. That probably make no sense.