Hi @JackANDJude and @alexpikkert
No need to fiddle settings to achieve the correct blinking sequence.
If you look carefully, you’ll notice a logic pattern 
Step 1 2 3 4 5 6 7 8
Clock. H. L. H. L. H. L. H. L
OUT. H. L. H. H. L. H. L. L
OK these are the bits used, up to you to connect them accordingly 😋
Wire, wire, power, LED, fork, pulse, latch, xor, inverter, latch
Happy puzzling !
And oh @alexpikkert, indeed, when you don’t have the XOR, it a true challenge to obtain the same blinking sequence.
An alternative is to use 5 Nand gates as pictured
NAND XOR GATE
Or the arduino after all 😜