Tequila
The AB review "provides" the following connections! I would have thought we ought to be able to find 2 other sites which have distilleries too!
"El Martineno Distillery, Tequila. A neo-classical complex constructed in 1870, the factory still contain old boilers and copper stills."
"Included in the site is the Teuchitlan site of Guachimontones. This consists of the ruins of a large residential complex dating from between 400 and 700 AD and contains ceremonial patios and platforms with houses or temples. In the centre is an extant multi-layered circular pyramid with four staircases, and nearby is one of the largest ball courts in Mesoamerica."
(So possible connections for Tequila are Neoclassical, Pyramids, Locations for playing sport)


Australian Fossil sites.
I hadn't realised just how far apart the 2 sites were in Australia –the opposite sides (N/S) of the country! So I suggest a connection along the lines of "Sites whose extremities are the furthest distance apart (over 1000kms)". 3 to start with are :-
Australian Fossil sites. Riverslea and Naracootra are approx 2012kms/1250 miles apart
Struve Arc – Fugelenaes (Norway) and Staro-Nekrassowka (Ukraine) are approx 2830kms/1758 miles apart
Great Wall of China. The extremities at Shanhaiguan and Jiayaguan are approximately 1824kms/1133 miles apart

Someone else can check the 2 Santiago de Compostela routes!

Purnululu
A problem! It was nominated on cultural criteria as well as natural and ICOMOS went along with iii and vi but asked for a deferral on a number of matters such as management plan etc AND also suggested that the park should ONLY be inscribed as a mixed site i.e if ICOMOS wanted it deferred for cultural aspects then it should be deferred in its entirety. UNESCO obviously didn't go along with this and inscribed it in 2003. Australia appears to have cut its losses and nothing more seems to have been done or said about pursuing the Cultural inscription.
Question – can/should/ we have (or have we in the past?) "connections" based on Cultural matters when it was inscribed as a Natural site only? If we can then we have "Minority community" and "Pictograph" connections.

The best possibility for a Natural connection appears to be something relating to the Karstitic aspect. We already have a "Category" for Karst (The IUCN evaluation mentions that there were 41 inscribed Karst Landscapes). Purnululu exhibits a special aspect regarding the shapes of the formations known as "Tower Karst" but I can only find Canaima inscribed with the same type - so not 3 unfortunately. Which leaves my suggestion regarding the rock type-
Non-Carbonate Karst Lanscapes . "Karst" is a land system that has been shaped, at least largely, by chemical solution. The vast majority of such landscapes worldwide were formed in limestone or other carbonate rocks. "It is now widely recognised that both quartz and amorphous silica are soluble in water, particularly at high temperatures. However, solution is much slower than in many other rocks such as the carbonates, gypsum and salt" (AB – IUCN). This phenomenon has only been identified by geo-morphologists since c1966,.
There are 3 WHS which exhibit it
Purnululu
Canaima
Wulingyuan

I just checked.

The furthest distance between sites on the route is 1,208km (Santiago - Basilique Notre-Dame, Chalons en Champagne) but that is across two separate WHS

The furthest distance in France is 814 km/ 506 miles (Ameins Cathedral - Eglise Paroissiale, Gavarnie nr. Mt Perdu)

In Spain the distance is slightly shorter 656 km/ 407 miles (Santiago - Canfranc)


These ones will make it in on the 1,000km +
Mountain railways of India 2,179km/ 1,354 miles (Nigrili - Shimla)

The Frontiers of the Roam Empire clocks in at 1,350 km /839 miles (Antonine Wall, Clydebank – Bavarian Limes, Hienheim on the Danube)

New Zealand Sub Antartic Islands 1,010km/627 miles (Bounty Islands - Auckland Islands)


These are short of the mark
Rock art of Iberian Penisula clocks in at 701km so is just short.

Imperial Palaces of the Ming and Qing Dynasties in Beijing and Shenyang is also short at 631km

NB. I can't work out if the Gondwana Rainforests of Australia will qualify as alot of the co-ordinates are incorrect on Google Earth. I will see if I can work it out soon. At the moment the biggest distnace is 450km but 13 sites are not mapped properly.

I had a look at the Gondwana Rainforests of Australia, and no they don't make it.
Though they would have done had Mt Dromedary Flora Reserve been included as originally propossed by Australia.