OK, one more time. First of all a single or pair of 555 timers (556) will not do what you want. Not with anything close to accurately. They don't work for times like an hour (3,600 seconds). You would use the 555 as the clock then add additional counter chips to get the ultra long delay you want. I suggest you read a 555 data sheet.
Then read this and understand what is going on.
Next, as I pointed out in the beginning of this thread there is a matter of timing and there is a matter of reversing polarity to your motor. So short of an H Bridge you tell me or anyone here how you want to reverse the motor's polarity? A crude but workable H Bridge can be built using 4 everyday generic switching transistors. Real crude but workable using 2 each 2N3904 and 2 each 2N3906. You are telling me you don't have access to basic switching transistors? How about a 2N2222 and a 2N2907?
I made it clear you don't need a PIC, the function of the PIC was the timing. Did you read any of that?
Use a 555 as a 1 second clock, then look at using a 4017 family chip (decade counter divider) to create your delay. I suggest you read and understand the 555 data sheet to calculate the R/C timing values.
Ron