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The little church beside Lake Thun is the reason to stop in Einigen. The village has a much smaller scale than Thun or Spiez, and a visit can be as simple as a look around the church and some time by the shore.
This is still a place of worship, so give services and ceremonies their space. If you continue walking, use the marked paths: there is no continuous lakeside footpath all the way to Spiez.