If I unlock an encrypted wallet for 359711509437336256 or less seconds, I can sign transactions with it:

    $ bitcoin-cli walletpassphrase "$x" 359711509437336256
    $ echo $?
    0
    $ bitcoin-cli signrawtransaction $tx | grep complete
      "complete": true

But if I unlock it for 359711509437336257 or more seconds, it appears to have unlocked but I can't sign any transactions:

    $ bitcoin-cli walletpassphrase "$x" 359711509437336257
    $ echo $?
    0
    $ bitcoin-cli signrawtransaction $tx | grep complete
    error code: -13
    error message:
    Error: Please enter the wallet passphrase with walletpassphrase first.

I don't know the significance of that number. It's nowhere near a power of 2.

I was trying to unlock the wallet effectively "forever", so put a big number. If I use too big a number (2^63 or more) I get an error message `JSON integer out of range` but for numbers between 359711509437336257 and 2^63-1 inclusive I get no error, but no actual unlocking.
"                             This is not part of the transaction, just kept in your wallet.\n"
            "4. \"comment_to\"         (string, optional) A comment to store the name of the person or organization \n"
            "                             to which you're sending the transaction. This is not part of the \n"
            "                             transaction, just kept in your wallet.\n"
            "5. subtractfeefromamount  (boolean, optional, default=false) The fee will be deducted from the amount being sent.\n"
            "                             The recipient will receive less bitcoins than you enter in the amount field.\n"
            "6. replaceable            (boolean, optional) Allow this transaction to be replaced by a transaction with higher fees via BIP 125\n"
            "7. conf_target            (numeric, optional) Confirmation target (in blocks)\n"
            "8. \"estimate_mode\"      (string, optional, default=UNSET) The fee estimate mode, must be one of:\n"
            "       \"UNSET\"\n"
            "       \"ECONOMICAL\"\n"
            "       \"CONSERVATIVE\"\n"
            "\nResult:\n"
            "\"txid\"                  (string) The transaction id.\n"
            "\nExamples:\n"
            + HelpExampleCli("sendtoaddress", "\"1M72Sfpbz1BPpXFHz9m3CdqATR44Jvaydd\" 0.1")
            + HelpExampleCli("sendtoaddress", "\"1M72Sfpbz1BPpXFHz9m3CdqATR44Jvaydd\" 0.1 \"donation\" \"seans outpost\"")
            + HelpExampleCli("sendtoaddress", "\"1M72Sfpbz1BPpXFHz9m3CdqATR44Jvaydd\" 0.1 \"\" \"\" true")
            + HelpExampleRpc("sendtoaddress", "\"1M72Sfpbz1BPpXFHz9m3CdqATR44Jvaydd\", 0.1, \"donation\", \"seans outpost\"")
        );
    ObserveSafeMode();
    
    
    pwallet->BlockUntilSyncedToCurrentChain();
    LOCK2(cs_main, pwallet->cs_wallet);
    CTxDestination dest = DecodeDestination(request.params[0].get_str());
    if (!IsValidDestination(dest)) {
        throw JSONRPCError(RPC_INVALID_ADDRESS_OR_KEY, "Invalid address");
    }