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.
continue;
            isminefilter mine = IsMine(*pwallet, address);
            if(!(mine & filter))
                continue;
            tallyitem& item = mapTally[address];
            item.nAmount += txout.nValue;
            item.nConf = std::min(item.nConf, nDepth);
            item.txids.push_back(wtx.GetHash());
            if (mine & ISMINE_WATCH_ONLY)
                item.fIsWatchonly = true;
        }
    }
    
    UniValue ret(UniValue::VARR);
    std::map<std::string, tallyitem> mapAccountTally;
    for (const std::pair<CTxDestination, CAddressBookData>& item : pwallet->mapAddressBook) {
        const CTxDestination& dest = item.first;
        const std::string& strAccount = item.second.name;
        std::map<CTxDestination, tallyitem>::iterator it = mapTally.find(dest);
        if (it == mapTally.end() && !fIncludeEmpty)
            continue;
        CAmount nAmount = 0;
        int nConf = std::numeric_limits<int>::max();
        bool fIsWatchonly = false;
        if (it != mapTally.end())
        {
            nAmount = (*it).second.nAmount;
            nConf = (*it).second.nConf;
            fIsWatchonly = (*it).second.fIsWatchonly;
        }