And while you're there, check the circuit for the sender. Cost for the sender for my 2008 truck at dealer is about $130 plus 1 hour to install. No cost to check the circuit, assuming you do it yourself. If your sender is good, but you have short or improper ground, you may see same readings, fluctuations you already have. Usual 3 wire setup, low reference, 5V reference, and a signal wire.
2008 Silverado LT, CCLB, Edge Insight CTS
2009 Arctic Fox 29-5T, Silver Fox Edition, Onan 3600 LPG generator