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.
"2. minconf           (numeric, optional, default=1) Only include transactions confirmed at least this many times.\n"
            "3. include_watchonly (bool, optional, default=false) Also include balance in watch-only addresses (see 'importaddress')\n"
            "\nResult:\n"
            "amount              (numeric) The total amount in " + CURRENCY_UNIT + " received for this account.\n"
            "\nExamples:\n"
            "\nThe total amount in the wallet with 1 or more confirmations\n"
            + HelpExampleCli("getbalance", "") +
            "\nThe total amount in the wallet at least 6 blocks confirmed\n"
            + HelpExampleCli("getbalance", "\"*\" 6") +
            "\nAs a json rpc call\n"
            + HelpExampleRpc("getbalance", "\"*\", 6")
        );
    ObserveSafeMode();
    
    
    pwallet->BlockUntilSyncedToCurrentChain();
    LOCK2(cs_main, pwallet->cs_wallet);
    const UniValue& account_value = request.params[0];
    const UniValue& minconf = request.params[1];
    const UniValue& include_watchonly = request.params[2];
    if (account_value.isNull()) {
        if (!minconf.isNull()) {
            throw JSONRPCError(RPC_INVALID_PARAMETER,
                "getbalance minconf option is only currently supported if an account is specified");
        }
        if (!include_watchonly.isNull()) {
            throw JSONRPCError(RPC_INVALID_PARAMETER,
                "getbalance include_watchonly option is only currently supported if an account is specified");
        }
        return ValueFromAmount(pwallet->GetBalance());