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.
const CBlockIndex* paltindex = nullptr; 
    int target_confirms = 1;
    isminefilter filter = ISMINE_SPENDABLE;
    if (!request.params[0].isNull() && !request.params[0].get_str().empty()) {
        uint256 blockId;
        blockId.SetHex(request.params[0].get_str());
        BlockMap::iterator it = mapBlockIndex.find(blockId);
        if (it == mapBlockIndex.end()) {
            throw JSONRPCError(RPC_INVALID_ADDRESS_OR_KEY, "Block not found");
        }
        paltindex = pindex = it->second;
        if (chainActive[pindex->nHeight] != pindex) {
            
            
            
            pindex = chainActive.FindFork(pindex);
        }
    }
    if (!request.params[1].isNull()) {
        target_confirms = request.params[1].get_int();
        if (target_confirms < 1) {
            throw JSONRPCError(RPC_INVALID_PARAMETER, "Invalid parameter");
        }
    }
    if (!request.params[2].isNull() && request.params[2].get_bool()) {
        filter = filter | ISMINE_WATCH_ONLY;
    }
    bool include_removed = (request.params[3].isNull() || request.params[3].get_bool());
    int depth = pindex ? (1 + chainActive.Height() - pindex->nHeight) : -1;
    UniValue transactions(UniValue::VARR);