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(
            "bumpfee \"txid\" ( options ) \n"
            "\nBumps the fee of an opt-in-RBF transaction T, replacing it with a new transaction B.\n"
            "An opt-in RBF transaction with the given txid must be in the wallet.\n"
            "The command will pay the additional fee by decreasing (or perhaps removing) its change output.\n"
            "If the change output is not big enough to cover the increased fee, the command will currently fail\n"
            "instead of adding new inputs to compensate. (A future implementation could improve this.)\n"
            "The command will fail if the wallet or mempool contains a transaction that spends one of T's outputs.\n"
            "By default, the new fee will be calculated automatically using estimatefee.\n"
            "The user can specify a confirmation target for estimatefee.\n"
            "Alternatively, the user can specify totalFee, or use RPC settxfee to set a higher fee rate.\n"