I don't know how to tell you this, so I'll just come right out and say it:
You need to ohm out that board and reverse engineer it to generate a schematic (I assume you don't have a link to a vendor for the board because I can't believe that you would have the bad judgement to post here on the forum without posting a link to the light board. That being the case, you need to get a pen and paper and draw a proper schematic and take a photo of it with your cell phone and post the photo. Until you post such a schematic , you will not get any help. If you had even the most basic experience in electronics you would have stated your request more specifically.
ie:
photo of block diagram showing jumpers
schematic symbol of switches shorting the jumpers
block diagram of arduino controlling the switches (perhaps using relays, or transistors)
etc etc etc
Sorry to say, but your video tells us nothing more than I already stated in one of my previous posts in this thread and which others have made similar , though different suggestions as a solution. There is nothing difficult about your question but as already stated, we need something more specific, like a schematic. If you actually are in possession of that light board , why have you not taken a close up photo directly above it (both sides) and posted these photos ? The only real mystery here is how you think we can help you without the details we need. (about the light board) or do we really need to know anything at all about the light board ?
If it were as simple as your video makes it sound, why would you waste time even talking about the motor or the light board and not simply ask:
"How can I use an arduino to close two SPST switches to short two 2-pin jumpers ?"
You are playing around with electronics. We need to know if you know anything about electronics so we know how to communicate with you. An SPST switch is one of the most basic concepts of electronics. The fact that there is no mention of this simple component in your request really suggests that you did not know the name of the component that you are asking for.
ie:
"I have two jumpers" (well, I'm calling them that but they aren't really 2-pin male headers as the term "jumper" would suggest. They are actually just two pieces of hookup wire sticking out of the bottom of my pcb"
"I want to short them with SPST switches/relays controlled by a uP (arduino)"
"The purpose is to replace two momentary switches (push buttons) with uP controlled contacts"
"I don't want to bore you with the reason i need to do this since it is irrelevant to my request"
"If I can control these two SPST switches/relays/transistors/optos with the arduino that will solve my problem (at the moment)"
Does that about sum it up ?
Also, you might clarify if the "jumpers" are actually factory made "jumpers" (2-pin male headers)(you do know what a male header is do you not ?) , or if they are not really "jumpers" (by definition) but simply pieces of wire sticking out of the bottom of the pcb that you have chosen to call "jumpers". This was not clear from the video.
I don't think we really need to know about the light board but if we do please post photos of both sides of the light board .
Please explain what you mean by "I don't really have anything to make a schematic ...etc"
Does this mean you don't have a pen and a blank piece of printer paper and a cell phone with a camera ?
or
does it mean you don't know how to draw a schematic ?
I think these are fair questions.
Seriously, am I being too harsh here ?