Yes, you can mirror your private keys and the wallets will work in lockstep by importing the same seed words from 1 wallet into the other .
Since one is wallet is a hw wallet than this isn't wise as you should not import the seed words in less secure environments . Those seed words should be on paper/metal and the hw wallet alone. If you are going to do this than at least use the passphrase feature where most of your savings is stored in the hidden passphrase protected wallet and the "synced" or "mirrored" wallet has some spending cash
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