This is more tricky than you would think. I've converted a number of plastic signs to LED. If you look at my facebook link you'll see them. The problem with LED strips or tubes is the light is more directional rather than spreading out, so you really need to place lights in the sign temporarily and see how it looks. Place them as far back as possible. Dont just go for it. What I've found is I end up putting more LEDs in than were there originally, that evens out the light, otherwise it can be like little spot lights or uneven. You have to be careful to get the right LEDs that are dimmable if you want dimmable and also to get the right dimmer switch too that matches. Amazon is a good source.
Lots of times I'm using LED tubes, some of the tubes are even painted off or blocked on the sides, making them really laser like. So looking at the description on amazon is really helpful, "light angle". There's lots of tubes on amazon, some you can daisy chain together to one included transformer which is cool, some have a back built in and then you can just mount from the back with double sided tape or screws whatever. When I'm using the daisy chainable tubes, I put them into the sign temporarily and change the distance between them until I get the look I like.
In the past, I've bought these if its helpful.
https://www.amazon.com/dp/B07FF7C7KF?ref_=ppx_hzsearch_conn_dt_b_fed_asin_title_8&th=1https://www.amazon.com/dp/B01CQ2ZKZO?ref_=ppx_hzsearch_conn_dt_b_fed_asin_title_3&th=1If you do LED strips, I'd get the white ones rather than the color change ones, the white is a little blue on the color change light strips.
