What we did, in a factory I used to work, is to employ a laptop. It already had the prerequisite VGA and HDMI outputs, you could change the resolution (within certain range) and the available test patterns were only limited by the ability to draw them or download it from the internet.
If a laptop is too large, perhaps a Raspberry Pi would be a solution. I've never personally worked with a Rasperry Pi, but understand that a project like yours is perfectly doable.
It only has a HDMI and composite video outputs, but building/purchasing an HDMI to VGA converter should be far easier.