My thoughts :- First check out the Vcc/0V pins - these tend to be constant on N pin packages. So once these have been tested, then there is no reason to check pins 7 and 14 (for 14pin TTL) .Once this has been sorted, then the pin 7 & 14 can be removed from the test schedule. Now moving over to the other pins. It is important that the "moving" probe is modified so it just makes a contact with all the pins, no sliding locking mechanism to actuate! First test would be interpin connections on IC, scan them at 1mS/pin, beep on short, stops test, displays input pin number (green ) and output pin number (red ) , LEDs must be spread out a bit 10mm + between AND labelled with number. Press button - test proceeds (to a count of 24 - for BIG ICs). At end all LEDs flash. Move test probe to next IC . It would be a nice idea to load the data into RAM as you go, just to double check at a later date!
Frank