Speedmaster 2013 Speedmaster Handlebar Wobble Issue

HI Everyone!
Newish to the forum and riding in general. I bought a beautiful used 2013 Speedmaster with 12k on the odometer. I noticed a handlebar wobble on deceleration when I take my hands off the bars any speed from about 35mph or higher. It's not a death wobble but noticeable. I cannot feel the wobble while my hands are on the bars at any speed.

I just replaced the tyres with stock Metzelers. Wobble went away temporarily for about 1k miles. I can't find anything wrong with it; nor can the dealer. Forks are good, the wheel bearing is good.

I replaced the fork oil. I do need to do brake pads soon. The bike has 40-liter fiberglass saddle bags on each side with an equal weight distribution of the contents inside.

Has anyone had this issue?

Is it just a trait of the bike?

I was told the bars should always be straight as an arrow/no wobble when taking hands off the bars while cruising.

 

Thank you MrOrange. I appreciate your response. I took it into my Triumph dealer. They inspected the wheel bearing - all good there. Replaced the fork oil, inspected/tightened/lubed the steering head bearing. Fork inspection all good. The wobble is gone now. So I am very happy. I will try a different brand of tyres next time around. But for now, we are cruisin smooth and straight.