How to wire 12v relay to operate projector screen?

Hello Everyone: Short form: Want my projector to control my electric projection screen (issue: On my projector I have a 12v trigger coming out of it, but my electric projector screen does not have a 12v input) What I do have is the option to add an Up and Down switch, to the screen controller box. What I... show more Hello Everyone:

Short form: Want my projector to control my electric projection screen (issue: On my projector I have a 12v trigger coming out of it, but my electric projector screen does not have a 12v input)

What I do have is the option to add an Up and Down switch, to the screen controller box.

What I was planning on doing is adding a 5 pin 12v relay, to control the up and down switch. I tested the screen and it will work with the down button continuosly pressed as well as the up button continuously pressed.

What I need is just confirmation that I'm wiring it correctly.

So the relay has 5 pins (and this is how I think it could work):

86 - 12v from projector (12v is continously feed when the projector is on)
30 - Ground from projector (for the 12v)
85 - Nothing connected

87 - The Down Switch (from the screen controller)
87a - The Up Switch (From the screen controller)
30 - the ground for the Up and Down Switch (from the screen controller)

From what I gather, When the relay is powered (ie 12v from projector) then the 87 and the 30 will close and in turn cause the screen to go down.

Then when the 12v is cut (ie the projector is turned off) then the 87a and the 30 will close, and in turn cause the screen to go up.

Brand new screen, just don't want to fry it doing something wrong.
Thanks in advance for you help.
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