PVCx looks alot like that foam-core paperboard used for school projects. PVCx is a closed-cell foam PVC core sandwiched between two thin layers of solid PVC. Because of this construction, it is much lighter-in-weight than solid PVC, and the foam core helps insulate and hold heat, so it works well with heat pads. It cleans well and is durable enough to be a floor of a snake cage.
It comes in various thicknesses. The common sizes are around 1/8" thick and 1/4" thick, but there exists 3/8" thick. For your app, the 1/8" stuff may work just fine, and the 1/4" stuff will certainly be fine.
You can cut with a saw meant for veneers or finish plywood, but you can also score it with a straight edge and blade (like 1/2 way deep) and break it along the line (it is soft, so it will not break like acrylic, but it pull apart like foam board does). You may then use the blade to carefully score the solid PVC coating that may not snap off. For your application, the score and break method is fine.
Sign shops have scraps, and the few I've been to will order me anything I am willing to pay for. A better way to go as mentioned is from plastic suppliers, like the one I mentioned before www.us-plastics.com, or it may be usplastics.com. I forgot. Google it.
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Mark