Some progress, I found a Chinese app for the JDY-08 and the two UUID's of interest are;
00002902-0000-1000-8000-00805f9b34fb (notificiation)
0000ffe1-0000-1000-8000-00805f9b34fb (tx/rx - looks like half duplex?)
Setting notifications to "1" puts the device into transparent mode
[A4:C1:38:77:28:E6][LE]> char-read-uuid 00002902-0000-1000-8000-00805f9b34fb
handle: 0x000b value: 00 00
[A4:C1:38:77:28:E6][LE]> char-write-cmd 0x000b 01 00
Now UART text comes through;
Notification handle = 0x000a value: 41 54 2b 4e 41 4d 45 0d 0a
Notification handle = 0x000a value: 41 54 2b 4e 41 4d 45 0d 0a
Notification handle = 0x000a value: 41 54 2b 42 41 55 44 0d 0a
Notification handle = 0x000a value: 31 30 0d 0a
Notification handle = 0x000a value: 31 0d 0a
However checking 0000ffe1-0000-1000-8000-00805f9b34fb offers no value, so perhaps this is a FIFO buffer.
Anyhow, doing a write to this char pumps it through to UART;
[A4:C1:38:77:28:E6][LE]> char-write-req 0x000a 01105D3A
Characteristic value was written successfully
So mission complete. Use the DISC pin to force a disconnect, or for a pre-configure prior to allowing a connection to go through.