Gas tank gauge sticking at 70%

On my 2004 FZ6 the gas gauge never shows the tank below about 70% full, unless when it's just topped off in which case it shows 100%. This became apparent about 2 weeks ago when I ran out of gas 1/2mi away from the gas station, while the LCD was still showing 70% full.

Since then I monitor the miles traveled after last filling, and try to refill every 150mi.

Any suggestions on how to go about fixing this myself?

I think the fuel level sending unit is part of the fuel pump so my guess would be replace that or try running a few bottles of Cheveron Techron in with the next couple of fillups.

has your bike sat for an extended period? maybe there is some varnish in the tank. if your bike is going to sit for an extended time you should put some fuel stabilizer in the tank

I had that problem with my '86 Saab, changing the sending unit didn't solve the problem.
Then, I went on vacation thru the Sonoran desert, and had to start buying a different brand of gas. The problem went away! My bass player at the time was a fuels dispatcher during the day, and from him I learned which stations bought which brand of gas from each manufacturer, and isolated the brand/stations I needed to stay away from (the Saab dealer was VERY glad to learn this info!).
So, try a few different brands of gas, that may clear it up.

The previous owner may have garaged the bike for longer stretches of time, but he did say that he ran the bike at least once a month.

Since I bought it, I've used a mix of U.S. gas stations (Shell, Chevron, etc.). I'll give Ferris' suggestion a shot and try Cheveron Techron in next fillups.