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() < 3 || request.params.size() > 5)
        throw std::runtime_error(
            "move \"fromaccount\" \"toaccount\" amount ( minconf \"comment\" )\n"
            "\nDEPRECATED. Move a specified amount from one account in your wallet to another.\n"
            "\nArguments:\n"
            "1. \"fromaccount\"   (string, required) The name of the account to move funds from. May be the default account using \"\".\n"
            "2. \"toaccount\"     (string, required) The name of the account to move funds to. May be the default account using \"\".\n"
            "3. amount            (numeric) Quantity of " + CURRENCY_UNIT + " to move between accounts.\n"
            "4. (dummy)           (numeric, optional) Ignored. Remains for backward compatibility.\n"