FYI : this is what I believe is the best guide for setting up a feeding schedule & diet for an ADULT bluetongue skink (any species) :
https://www.completecritter.com/blue-tongue-skink.html , I was put onto this my reptile vet many years ago when my old BTS George & Mildred were both small juveniles .
I don't give my skinks mice (pinkies) EVER ,as they are WAY TOO FATTENING and an impaction risk.
My vet recommend only softened VetaFarm lizard pellets, chicken eggs (while raw, hard boiled (whiles and yoke), and unseasoned scrabbled ) , and boiled lean chicken mince as protein sources other than insects , and advised against cat or dog food for a captive skink other than as treats or maybe a small part of the diet.
Note = the dietary requirements is highly dependent on the skinks age …. ie a baby needs an entirely live insect diet , a juvenile needs mostly live insects in it's diet.
My adult BTSs' diet has no commercial cat or dog food (ever) , but includes a couple of large silkworms each per day + fruit & veg + some crickets ( crush the crickets' heads to make them easier for the skinks to catch them), I also buy in live human food grade snails on a monthly basis & give superworms & egg & banana as treats.