One strong indicator of globalization is trade. The WTO maintains a set of global trade indicators, which has data on trade flows, trade disputes and tariff levels going back to 1948.
Some variables I would be interested in seeing tracked include:
Access to public utilities. I'm looking for global power, water, data, transport (both goods and people) and economic networks.
Relatedly: Does such an index exist?
Relatedly: What are relevant graphs / metrics / data on those variables?