You can achieve it with bisync however it has its quirks - maybe this is why it is experimental. Initial --resync run seems not to respect modtime and just overwrites Path1 with Path2
make local empty folder:
rclone bisync local_path remote: --resync
now when files change and you run:
rclone bisync local_path remote:
it should behave as expected.
You can also run rclone copy with below flag:
-u, --update Skip files that are newer on the destination