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.
{
    CWallet * const pwallet = GetWalletForJSONRPCRequest(request);
    if (!EnsureWalletIsAvailable(pwallet, request.fHelp)) {
        return NullUniValue;
    }
    if (request.fHelp || request.params.size() < 1 || request.params.size() > 3)
        throw std::runtime_error(
                            "fundrawtransaction \"hexstring\" ( options iswitness )\n"
                            "\nAdd inputs to a transaction until it has enough in value to meet its out value.\n"
                            "This will not modify existing inputs, and will add at most one change output to the outputs.\n"
                            "No existing outputs will be modified unless \"subtractFeeFromOutputs\" is specified.\n"
                            "Note that inputs which were signed may need to be resigned after completion since in/outputs have been added.\n"
                            "The inputs added will not be signed, use signrawtransaction for that.\n"
                            "Note that all existing inputs must have their previous output transaction be in the wallet.\n"
                            "Note that all inputs selected must be of standard form and P2SH scripts must be\n"