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() > 0)
        throw std::runtime_error(
            "getrawchangeaddress\n"
            "\nReturns a new Bitcoin address, for receiving change.\n"
            "This is for use with raw transactions, NOT normal use.\n"
            "\nResult:\n"
            "\"address\"    (string) The address\n"
            "\nExamples:\n"
            + HelpExampleCli("getrawchangeaddress", "")
            + HelpExampleRpc("getrawchangeaddress", "")
       );
    LOCK2(cs_main, pwallet->cs_wallet);
    if (!pwallet->IsLocked()) {
        pwallet->TopUpKeyPool();
    }
    CReserveKey reservekey(pwallet);
    CPubKey vchPubKey;
    if (!reservekey.GetReservedKey(vchPubKey, true))
        throw JSONRPCError(RPC_WALLET_KEYPOOL_RAN_OUT, "Error: Keypool ran out, please call keypoolrefill first");
    reservekey.KeepKey();
    CKeyID keyID = vchPubKey.GetID();
    return EncodeDestination(keyID);
}
UniValue setaccount(const JSONRPCRequest& request)