Why do both lights stay on when the 4 wheel drive is engaged? sometimes it does not go in the lights

Sounds like the vacuum/electrical switch that kicks over the 4WD is going out. I would take this to a mechanic and have it checked out. It's not a hard or expensive fix but it could be either wiring related or switch related.

this propblem can be caused by 1 the encoder motor/transfercase motor 2 the transfercase switch 3 vaccum actuator under battery tray 4 broken cable from actuator to front diff. now we know the possible problems lets check them individualy fist the encoder motor when your in nutral and press the 4hi button does it flash and just never go in? can you hear an electric motor? after you press 4hi get undernieth the blazer and check if you can turn the front drive shaft by hand? in not this is a good thing and means your transfercase is locked in four wheel drive. if you can turn the drive shaft by hand i would replace the encodermotor (any where from 130$-150$ at a parts store and you do the work your self second is testing the vaccum lines after your transfer case is locked there is one line going from the back of the plenium to the switch on top of the transfercase when the engine is running it should have vaccum when you put it in 4hi it switches the switch and provides vaccum to the front actuator under the batery tray (this is the hose i think one of the privious posters talked about) make sure there is vaccum to the hose when in four wheel drive and if there is no vaccum i would replace the vaccum switch (10$-20$ at parts store and you do the work your self) if there is vaccum then you need to test the actuator it self you should be able to see it move when 4wheel drive is turnd on and off if it dont move the diphram could be tore and if it does move then very very very unliky your cable from the actuator to the front differntial is broken and i dont know what would be wrong hope this helps let us know when/if you fix it *the picture is of the actuator under the tray p.s dont listen to the post before me i would fix it myself if i was you