UTC+5:30 is now used in the whole India including Sikkim. What time zone was used before 1975? According to the geographical location of Sikkim I guess UTC+6 might be used there. I searched online but couldn't find any information that gives a clear answer.
One of the main imperatives for standardised time in India was the railways. Since the pre-1975 Kingdom of Sikkim had no railways, I suspect it may not have had standardised time either.
A lack of standardised time means that each settlement uses its "local solar time" which means that noon is when the sun is at its highest. They use that to set their clocks and work from there.