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.
lockUnspents = options["lockUnspents"].get_bool();
        if (options.exists("feeRate"))
        {
            coinControl.m_feerate = CFeeRate(AmountFromValue(options["feeRate"]));
            coinControl.fOverrideFeeRate = true;
        }
        if (options.exists("subtractFeeFromOutputs"))
            subtractFeeFromOutputs = options["subtractFeeFromOutputs"].get_array();
        if (options.exists("replaceable")) {
            coinControl.signalRbf = options["replaceable"].get_bool();
        }
        if (options.exists("conf_target")) {
            if (options.exists("feeRate")) {
                throw JSONRPCError(RPC_INVALID_PARAMETER, "Cannot specify both conf_target and feeRate");
            }
            coinControl.m_confirm_target = ParseConfirmTarget(options["conf_target"]);
        }
        if (options.exists("estimate_mode")) {
            if (options.exists("feeRate")) {
                throw JSONRPCError(RPC_INVALID_PARAMETER, "Cannot specify both estimate_mode and feeRate");
            }
            if (!FeeModeFromString(options["estimate_mode"].get_str(), coinControl.m_fee_mode)) {
                throw JSONRPCError(RPC_INVALID_PARAMETER, "Invalid estimate_mode parameter");
            }
        }
      }
    }
    
    CMutableTransaction tx;
    bool try_witness = request.params[2].isNull() ? true : request.params[2].get_bool();