Abrupt climate change events during glacial times have distinct tropical imprints, despite their cause being at high latitudes. The mechanisms by which high latitudes affect low latitudes are currently unclear. We present climate model simulations of a set of different abrupt events and find changes in tropical rainfall can not be comprehensively explained by either changes in sea ice extent or ocean circulation. Changes in tropical meridional temperature gradients are the clearest way to explain tropical rainfall changes across all events. We find some tropical regions are unlikely to record Heinrich Events because the rainfall is moved far enough away from them during stadial periods that they are insensitive to further change. Greenland temperature responds linearly to Atlantic sea ice extent suggesting that the absence of change in Greenland temperature during Heinrich Events implies no sea ice expansion, despite major changes in the climate system elsewhere.