Welcome to the site. The GL1200's don't suffer from electrical problems. Many just suffer from age and neglect. If there's a weak spot, it's the stator - but again, many stator failures are due to heavy loads imparted from old, neglected, corroded, high resistance connections in the charging circuit. If it's working now, there are a number of preventive and/or corrective actions that can be taken to prevent issues. I had an '84 Aspencade. If I were to go for another GL1200, it would be an Interstate as I'm not a fan of the digital instruments.
At the end of the day, it'll still be a 30 year old machine with potential issues around the corner. But, it'll be more reliable and long-legged than ANY OTHER 30 year old machine you might consider.