For backlits, your best bet is always going to be to use a good quality translucent cut vinyl, it produces the best results day and night. However if the design doesn't allow for that, you can print on translucent white vinyl.
The problem with printing translucent
signs is that the inks are translucent so when you back light a standard print it looks very washed out. There is a way around d this that involves printing on 2 seperate sheets and carefully lining them up, but your material costs double and your labour cost goes up.
Double printing is a way of laying down 2 times as much ink as normal so when the
sign is backlit the colours look correct, however during the day the colours are too dark
TL;DR use a translucent cut vinyl where possible as your results will be much nicer.