looks like a pretty old style projecting lightbox mate.
but your pretty much correct. if you remove the screws down "one side" nearest us in the picture. you will have removed an "L" shaped trim. at this point you should be able to slide out the peice of acrylic completey t expose all the tubes. here it should just be a case of removing and renewing. slide the panel back in and tighten the screws.
sometimes you need to loosen (not remove) the screws along the top and bottom "at one side" because the acrylic sheet maybe jammed for various reasons like gunk build-up etc
also, is it a bulb out? sometimes the transformers can get exposed to water and the like in old signs. just be careful this isnt the case. often cheaper to renew the whole box rather than bulbs and transformer etc by this is just mean watch you dont open a can of worms of problems for yourself.