Why is Montresor carrying a trowel under his cloak in "The Cask of Amontillado"?

In Edgar Allan Poe's "The Cask of Amontillado" every detail has a logical explanation because the author worked out the plot with such care, although he does not explain everything to the reader. A good example of Poe's craftsmanship concerns the very obvious question: Why is Montresor carrying a trowel under his cloak? Montresor plans to lure Fortunato to a specific location deep under the ground where he has already gathered stones and prepared mortar for walling his victim up in a niche where there are two short chains attached to the granite wall. The chains have probably been there for centuries and have been used by noblemen to dispose of enemies in the same way that Montresor plans to dispose of Fortunato. But why doesn't Montresor leave the trowel with the stones and the mortar?

A trowel is a rather delicate and sensitive tool made of steel. If left in that dank underground environment it would quickly become rusted. He counted on the extreme dampness and the covering of moist human bones to keep his mortar soft, but he can't leave a fine steel trowel in the same dripping environment. He wants it to be in good condition because he is planning to do a first-class job of entombing  and concealing his victim. After he has constructed the wall, he covers the rough stones with plaster and smooths the entire surface to make it look as if it is only part of the entire granite wall. This is how Poe describes the finishing touches.

I hastened to make an end of my labour. I forced the last stone into its position; I plastered it up. Against the new masonry I reerected the old rampart of bones. For the last half of a century no mortal has disturbed them.

Montresor did not want to leave the trowel underground, but he wanted to have it handy when he brought Fortunato to the niche. He could hardly have kept it upstairs in his palazzo and gone to fetch it when he brought his victim home. How did he know he would encounter Fortunato that night? He didn't. But he was out looking for him. And finding him drunk and reveling on the streets was not at all surprising.

As far as his showing Fortunato the trowel as "proof" that he was a Mason, this was unanticipated. Montresor had to be a little tipsy himself because he had to drink with Fortunato--although certainly not as much. Once he has his enemy under the ground he feels relieved, elated, jubilant. He makes zany gentures. He invents a ludicrous coat of arms and Latin motto to go with it. He exposes the trowel and claims to be a Mason. The hardest part of his plan is behind him. He can kill Fortunato any time he wants. He has a rapier under his cloak. It was not necessary to say that Fortunato was unarmed because the man was wearing a tight-fitting jester's costume with which a sword would be completely inappropriate and impossible to conceal.

So Montresor was carrying his trowel under his cloak because he wanted to have it instantly accessible and in perfect condition. He didn't know for certain that he would encounter Fortunato on that particular night, but he had good reason to hope so. If not, the carnival would last for more nights and Montresor could continue to search for his victim with his trowel in readiness.