The dash staying on has me stumped. Are your grounds good? Did it function normal before swapping to new signals? I'm more of a Honda guy when it comes to electronics, but I wonder if Suzuki Designed the gauge cluster to Illuminate the dash light if it senses a blown turn signal bulb. Dead regular bulb, like an LED swap may cause the dash light to stay on. Let us know the results with the LED relay. I reread the OP and he doesn't clarify if he used an LED relay. In addition, his comments about power lead me to believe he saw power going to the front running light filaments not knowing about the second filament for the turn signal (disconnected). I think your on the right track Murdered.