There are a number of joints & holes in the floor & firewall, & of course around the doors. One of the restoration projects to be done is replace all grommets, sealing strips & such, & add sealing where it is needed. Forty year old rubber doesn't seal very well. Many older cars have had some of the seals left out by the owner as the car was worked on over the years. Look at a good illustrated catalog to identify the rubber bits that may be damaged or missing on your car. Rust holes are another distinct possibility. Sometimes the heater or it's hoses leak & drip water inside the car. Water can run down the windshield posts. The convertible models can have plugged drain channels.
If the car is truly renewed, including all rubber bits, they don't leak. On a comical note, my car previously had a very thorough body off restoration. The metal work & paint was flawless & everything well aligned. No signs of rust. Don't know whether the previous owner ran out of money or just got in a hurry. The car was reassembled with absolutely no rubber seals, gaskets, grommets, or anything else. I've spent countless dollars & hours researching & installing all of the rubber & sealing bits that were left out. Just look in a Moss catalog, anything made of rubber was left out except the tires & they were 10 years old. It's as hard to find out what is missing as it is to replace it.
The standard trick is, in a darkened garage, remove interior rugs etc to bare metal, put a light under the hood & under the car sections & look carefully for any light showing through. Spray some water on the outside sections & look for water entry. If everything is done right there are no water leaks.
If you don't have a clue, the Moss illustrated catalog & the Anderson - Moment restoration book will help a lot.
The only time I have had to unsnap the carpets was when I got caught in a rainstorm with the top down.
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