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.
std::vector<COutPoint> outputs;
    outputs.reserve(output_params.size());
    for (unsigned int idx = 0; idx < output_params.size(); idx++) {
        const UniValue& o = output_params[idx].get_obj();
        RPCTypeCheckObj(o,
            {
                {"txid", UniValueType(UniValue::VSTR)},
                {"vout", UniValueType(UniValue::VNUM)},
            });
        const std::string& txid = find_value(o, "txid").get_str();
        if (!IsHex(txid)) {
            throw JSONRPCError(RPC_INVALID_PARAMETER, "Invalid parameter, expected hex txid");
        }
        const int nOutput = find_value(o, "vout").get_int();
        if (nOutput < 0) {
            throw JSONRPCError(RPC_INVALID_PARAMETER, "Invalid parameter, vout must be positive");
        }
        const COutPoint outpt(uint256S(txid), nOutput);
        const auto it = pwallet->mapWallet.find(outpt.hash);
        if (it == pwallet->mapWallet.end()) {
            throw JSONRPCError(RPC_INVALID_PARAMETER, "Invalid parameter, unknown transaction");
        }
        const CWalletTx& trans = it->second;
        if (outpt.n >= trans.tx->vout.size()) {
            throw JSONRPCError(RPC_INVALID_PARAMETER, "Invalid parameter, vout index out of bounds");
        }
        if (pwallet->IsSpent(outpt.hash, outpt.n)) {
            throw JSONRPCError(RPC_INVALID_PARAMETER, "Invalid parameter, expected unspent output");
        }
        const bool is_locked = pwallet->IsLockedCoin(outpt.hash, outpt.n);