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)
        throw std::runtime_error(
            "lockunspent unlock ([{\"txid\":\"txid\",\"vout\":n},...])\n"
            "\nUpdates list of temporarily unspendable outputs.\n"
            "Temporarily lock (unlock=false) or unlock (unlock=true) specified transaction outputs.\n"
            "If no transaction outputs are specified when unlocking then all current locked transaction outputs are unlocked.\n"
            "A locked transaction output will not be chosen by automatic coin selection, when spending bitcoins.\n"
            "Locks are stored in memory only. Nodes start with zero locked outputs, and the locked output list\n"
            "is always cleared (by virtue of process exit) when a node stops or fails.\n"
            "Also see the listunspent call\n"
            "\nArguments:\n"
            "1. unlock            (boolean, required) Whether to unlock (true) or lock (false) the specified transactions\n"
            "2. \"transactions\"  (string, optional) A json array of objects. Each object the txid (string) vout (numeric)\n"
            "     [           (json array of json objects)\n"
            "       {\n"
            "         \"txid\":\"id\",    (string) The transaction id\n"
            "         \"vout\": n         (numeric) The output number\n"
            "       }\n"