House electrical troubleshoointg question

[kerry]

Tenant called describing a problem. She turns on living room light. I works for a while then cuts out. When it cuts out, two other fixtures also cut out. I assume these are downstream. I'm guessing there's a poor connection that fails when it gets warm. My question is: Where is the connection likely to be? Are the downstream fixtures more likely to draw their hot feed from the switch box or the fixture box? I'm thinking the switch box and speculating that one of those push in connectors in the switch is cutting out.