Control HDMI Switch with Arduino Uno board

I have a basic HDMI switch, cheap one off Amazon (link below), and I want to control it with my Arduino Uno board. It is a 3 input to 1 output switch. So if it has all 3 plugs and the output linked to a TV, I want the Uno to control which feed is being sent to the TV and even no feed at all sent. There is no power in the switch, it is runs off the 5v power from the HDMI cord plugged into it.

I am very new to this and therefore a novice. I am thinking I have to control the power of the HDMI switch with the Uno board, and let that power dictate which feed to send in the HDMI switch output. However, I have no idea how to do this, and I could be completely wrong. Any feedback is greatly appreciated.

Thanks.

I took a look at the amazon link. I think you can probably pull off the button and connect it to the normally open part of a relay. And then just send the relay 5v for a second or so when you want to change sources.

This is what the HDMI switch looks like opened up.

moderator added image link

Put a voltage meter across each lead seperately to ground. One probably reads 3.3v or 5v always and the other is zero. And then when you press it down you should get non zero on both. Alternatively you can use the ampmeter across the two pins on the button.