Rudy Giuliani's taking his time picking a new hair dye ... eyeing the ingredients on the back with suspicion -- and, he's got good reason to be cautious.

The former mayor of New York City hit up a Walmart in Secaucus, New Jersey Saturday afternoon ... pulling up in a mobility scooter with an aide by his side.

The two are in the haircare section -- you can see the products on the shelf in front of him -- and Giuliani is scrutinizing the back of what we're told is hair dye.

Unclear what Rudy's looking for here ... but, he might be concerned about another awkward interaction if his dye job starts running again.

Remember ... in the aftermath of the 2020 election, Giuliani was working for Donald Trump to prove widespread voter fraud had swung the results.

During one press conference, the heat started to get to RG ... and, while he repeatedly wiped his brow, it got so hot that hair dye started to run in a line down his cheek. The moment was satirized on shows like "Saturday Night Live" and "It's Always Sunny in Philadelphia."

The past few years have been difficult for Giuliani ... who surrendered to authorities in August 2023 and hit with multiple charges like engaging in criminal conspiracies and breaking Georgia's racketeering act after he allegedly trying to interfere with federal election results in the state.

He was also ordered to pay $146 million to two Georgia election officials he defamed ... and, he had to declare bankruptcy because of it. Giuliani was also disbarred in New York last year.

Looks like Giuliani's looking to add a little more color to his hair ... hopefully it sticks!