Hi!
That looks similar to a controller I've seen in a Comfortmaker furnace. The controller in that application was known as "The General
90" and was also made in Mexico. Although it had fewer components on it, the connectors were very similar and in about the same positions.
It's mentioned on that particular controller that no service is possible, so don't expect any help from the manufacturer. They'll probably try to sell you another one.
What I'd look at are any and all capacitors, to see if any have failed. If the module is mounted on the furnace blower, it should have very good cooling, so heat related failures are unlikely as long as the blower is running. :-) But if it's not in the path of some airflow, or if it's near a burner, the capacitors are a likely candidate for problems. They won't stand the heat, as the electrolyte dries up and makes the capacitor fail. If you do not have a capacitor checker, look for bulged tops or brown flaky residue on the capacitor tops.
If that doesn't turn anything up, the glue that seems to be all over that board should be investigated. Some of it may have turned conductive over time. This will produce strange results.
Finally, examine the relays. See if you can pop them open without undue violence. You may find burned contacts that don't do what they are supposed to do reliably. Fixing this may be a little difficult-- usually some gentle abrasion of the contacts to clean the burnt material away will work, but eventually you will need a new relay as the damage will eventually return. If the manufacturer of the relays is still making them, and they are not a custom part, you may be able to get them.
William