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() > 2)
    {
        std::string msg = "addwitnessaddress \"address\" ( p2sh )\n"
            "\nAdd a witness address for a script (with pubkey or redeemscript known). Requires a new wallet backup.\n"
            "It returns the witness script.\n"
            "\nArguments:\n"
            "1. \"address\"       (string, required) An address known to the wallet\n"
            "2. p2sh            (bool, optional, default=true) Embed inside P2SH\n"
            "\nResult:\n"
            "\"witnessaddress\",  (string) The value of the new address (P2SH or BIP173).\n"
            "}\n"
        ;
        throw std::runtime_error(msg);
    }
    {
        LOCK(cs_main);
        if (!IsWitnessEnabled(chainActive.Tip(), Params().GetConsensus()) && !gArgs.GetBoolArg("-walletprematurewitness", false)) {
            throw JSONRPCError(RPC_WALLET_ERROR, "Segregated witness not enabled on network");
        }
    }
    CTxDestination dest = DecodeDestination(request.params[0].get_str());
    if (!IsValidDestination(dest)) {
        throw JSONRPCError(RPC_INVALID_ADDRESS_OR_KEY, "Invalid Bitcoin address");
    }