what does "a spare handful of times"mean? does it mean=seldom?
He liked his ties. It wasn’t as if he had an emotional attachment, but he liked having a variety. Choices.
Which still didn’t explain why he’d brought them all to the beach, especially when he’d worn a tie a spare handful of times in the last six months.
Okay, maybe a slight emotional attachment. He’d won court cases in these ties, and lost a few. He’d selected one every day of his working life. Had loosened them during late nights at the office. Knotted and unknotted them countless times.

Question

what does "a spare handful of times"mean? does it mean=seldom?
He liked his ties. It wasn’t as if he had an emotional attachment, but he liked having a variety. Choices. 
Which still didn’t explain why he’d brought them all to the beach, especially when he’d worn a tie a spare handful of times in the last six months. 
Okay, maybe a slight emotional attachment. He’d won court cases in these ties, and lost a few. He’d selected one every day of his working life. Had loosened them during late nights at the office. Knotted and unknotted them countless times.

Answer

Yes, I think you are correct, the idea is seldom - although it is more like 'a few'.
A handful would be maybe 3-4 times. A spare handful would be less than that. It certainly isn't a common expression, but is relatively clear from the context.