I was experimenting with the 'Radial / None' option for wire connections, which didn't work the way I hoped.

Then I tried the 'Rotation' option in the 'Block Authoring Palettes - All Palettes' pop up box. I was concerned that it only let the rotation go in the counter-clockwise direction, but went ahead, saved it, and inserted it into the library to test. With no luck, it did not rotate on it's own. I am attaching a screen shot of me using the 'Rotation' function.

Is there something I am missing with either of those two functions to "auto-rotate" the symbol, or is it a different function altogether? 

I apologize if I did not submit this question to the right section, I am new at forums.

However, I solved my problem by finding the files for the icons that AutoCAD E uses for its library, opening each of them, and replacing their symbols with my company's symbols, and then moving around the attributes to fit the new icon. 

First I insert the symbol that I want to use, say a fuse, I insert it once horizontally, and once vertically. I double click the first one and see the name of the block. I search for that block in the library path (jic125) HFU1 (H=horizontal, FU=device name, 1=parent). I open the file, change it how I want it to appear, making sure that the centre of the symbol stays at (0,0) for the insertion point. I save it, go back to the drawing page, delete the icon I just worked on, purge, and then reinsert it to make sure it was formatted correctly. Then I go back to the jic125 and open VFU1 for the vertical one, and do the same thing. Then when I go to insert the symbol, it appears as my company's symbols, while still self-orienting itself to the horizontal or vertical wire I placed it on.